input stringlengths 50 25.7k | output_prefix stringlengths 0 8.1k | output stringlengths 8 1.79k | next_output_prefix stringlengths 12 8.13k | next_output stringlengths 8 1.79k ⌀ | terminal int64 0 1 | completion int64 0 0 | trajectory int64 0 6.05k | step int64 0 74 | label int64 0 1 | reward int64 0 1 | is_chosen bool 1
class | rtg float64 0 5 | undiscounted_rtg bool 2
classes | text stringlengths 94 8.49k | __index_level_0__ int64 0 1.94k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP] | 0 | 0 | 5,225 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 0 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP] |
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP] | 0 | 0 | 5,225 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over... | 1 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP] |
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP]
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP] |
[STEP] 3. Right. So the reflected center is $(-5,6)$. [/STEP] | 0 | 0 | 5,225 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over... | 2 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP]
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP] |
[STEP] 3. Right. So the reflected center is $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP]
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP]
[STEP] 3. Right. So the reflected center is $(-5,6)$. [/STEP] |
[STEP] # Answer
(-5,6) [/STEP] | 0 | 0 | 5,225 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over... | 3 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP]
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP]
[STEP] 3. Right. So the reflected center is $(-5,6)$. [/STEP] |
[STEP] # Answer
(-5,6) [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over $y=x$, we just switch the $x$ and $y$ coordinates. [/STEP]
[STEP] 2. So the center of the reflected circle is $(-5,6)$. [/STEP]
[STEP] 3. Right. So the reflected center is $(-5,6)$. [/STEP]
[STEP] # Answer
(-5,6... | null | 1 | 0 | 5,225 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect it over... | 4 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP] |
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP] |
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP] | 0 | 0 | 5,226 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP] | 5 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP] |
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP] |
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP] |
[STEP] 2. That means the new center of the circle is at $(-5,6)$. [/STEP] | 0 | 0 | 5,226 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect ... | 6 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP] |
[STEP] 2. That means the new center of the circle is at $(-5,6)$. [/STEP] |
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP]
[STEP] 2. That means the new center of the circle is at $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,226 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect ... | 7 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP]
[STEP] 2. That means the new center of the circle is at $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect that across the line $y=x$, the new $x$ coordinate is the old $y$ coordinate and the new $y$ coordinate is the old $x$ coordinate. [/STEP]
[STEP] 2. That means the new center of the circle is at $(-5,6)$. [/STEP]
[... | null | 1 | 0 | 5,226 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the original center of the circle is at $(6,-5)$. [/STEP]
[STEP] 1. And when we reflect ... | 8 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, to find the center of the image circle, I just need to switch the $x$ and $y$ coordinates of the original center.
[* 0. The original center was at $(6,-5)$, so the new center is at $(-5,6)$. [/STEP] | 0 | 0 | 5,227 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordina... | 9 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, to find the center of the image circle, I just need to switch the $x$ and $y$ coordinates of the original center.
[* 0. The original center was at $(6,-5)$, so the new center is at $(-5,6)$. [/STEP] |
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, to find the center of the image circle, I just need to switch the $x$ and $y$ coordinates of the original center.
[* 0. The original center was at $(6,-5)$, so the new center is at $(-5,6)... |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,227 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordina... | 10 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, to find the center of the image circle, I just need to switch the $x$ and $y$ coordinates of the original center.
[* 0. The original center was at $(6,-5)$, so the new center is at $(-5,6)... |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, to find the center of the image circle, I just need to switch the $x$ and $y$ coordinates of the original center.
[* 0. The original center was at $(6,-5)$, so the new center is at $(-5,6)... | null | 1 | 0 | 5,227 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I know that reflecting a point across the line $y=x$ means swapping its $x$ and $y$ coordina... | 11 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So the center of the image circle will have coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,228 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 12 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,228 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 13 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So the center of the image circle will have coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,228 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 14 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP] | 0 | 0 | 5,229 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 15 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP] |
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP] | 0 | 0 | 5,229 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 16 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP] |
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP] |
[STEP] 3. Right. Now we can find the coordinates of the other two circles. [/STEP] | 0 | 0 | 5,229 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 17 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP] |
[STEP] 3. Right. Now we can find the coordinates of the other two circles. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 4. The circle that is tangent to the line $y=x$ has a center at $(0,0)$. [/STEP] | 0 | 0 | 5,229 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 18 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 4. The circle that is tangent to the line $y=x$ has a center at $(0,0)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 5. And the circle that is tangent to the line $x=6$ has a center at $(6,6)$. [/STEP] | 0 | 0 | 5,229 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 19 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 5. And the circle that is tangent to the line $x=6$ has a center at $(6,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 6. Right. Now we just need to find the coordinates of the circle that is tangent to the line $y=-5$. [/STEP] | 0 | 0 | 5,229 | 5 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 20 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 6. Right. Now we just need to find the coordinates of the circle that is tangent to the line $y=-5$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 7. The center of that circle is $(-5,-5)$. [/STEP] | 0 | 0 | 5,229 | 6 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 21 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 7. The center of that circle is $(-5,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 8. So the coordinates of the center of the fourth circle are $-5,-5$. [/STEP] | 0 | 0 | 5,229 | 7 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 22 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 8. So the coordinates of the center of the fourth circle are $-5,-5$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 9. Right. Now we can draw the four circles. [/STEP] | 0 | 0 | 5,229 | 8 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 23 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 9. Right. Now we can draw the four circles. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 10. The first circle has a center at $(6,-5)$ [/STEP] | 0 | 0 | 5,229 | 9 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 24 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 10. The first circle has a center at $(6,-5)$ [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 11. The second circle has a center at $(-5,6)$ [/STEP] | 0 | 0 | 5,229 | 10 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 25 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 11. The second circle has a center at $(-5,6)$ [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 12. The third circle has a center at $(0,0)$ [/STEP] | 0 | 0 | 5,229 | 11 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 26 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 12. The third circle has a center at $(0,0)$ [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 13. The fourth circle has a center at $(-5,-5)$ [/STEP] | 0 | 0 | 5,229 | 12 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 27 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 13. The fourth circle has a center at $(-5,-5)$ [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 14. And since the radius of all the circles are the same, they are all congruent. [/STEP] | 0 | 0 | 5,229 | 13 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 28 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] 14. And since the radius of all the circles are the same, they are all congruent. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] # Answer
-5,6 -5,-5 [/STEP] | 0 | 0 | 5,229 | 14 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 29 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... |
[STEP] # Answer
-5,6 -5,-5 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that over the line $y=x$, then the new center of the circle is $(-5,6)$. [/STEP]
[STEP] 2. So the coordinates of the center of the image circle are $-5,6$. [/STEP]
[STEP] 3. Right. Now we can find the coordinates of the... | null | 1 | 0 | 5,229 | 15 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. And if we reflect that ... | 30 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,230 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coo... | 31 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,230 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coo... | 32 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,230 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect the center of the circle about the line $y=x$, I need to swap its $x$ and $y$ coo... | 33 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] | 0 | 0 | 5,231 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 34 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] | 0 | 0 | 5,231 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 35 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP]
[STEP] # Answer
-5, 6 [/STEP] | null | 1 | 0 | 5,231 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 36 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] | 0 | 0 | 5,232 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 37 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] | 0 | 0 | 5,232 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 38 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,232 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 39 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,232 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 40 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP] | 0 | 0 | 5,233 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STE... | 41 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP] |
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP] | 0 | 0 | 5,233 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STE... | 42 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP] |
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP]
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP] |
[STEP] 3. I also need to include the radius of the circle, but the problem does not mention it. [/STEP] | 0 | 0 | 5,233 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STE... | 43 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP]
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP] |
[STEP] 3. I also need to include the radius of the circle, but the problem does not mention it. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP]
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP]
[STEP] 3. I also need to include the radius of the circle, but the ... |
[STEP] # Answer
x=-5, y=6 [/STEP] | 0 | 0 | 5,233 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STE... | 44 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP]
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP]
[STEP] 3. I also need to include the radius of the circle, but the ... |
[STEP] # Answer
x=-5, y=6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center is $(-5,6)$. [/STEP]
[STEP] 2. I can write this as $x=-5, y=6$. [/STEP]
[STEP] 3. I also need to include the radius of the circle, but the ... | null | 1 | 0 | 5,233 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates. [/STE... | 45 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,234 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 46 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,234 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 47 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,234 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 48 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP] | 0 | 0 | 5,235 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 49 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP] |
[STEP] 2. That's our answer. [/STEP] | 0 | 0 | 5,235 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect th... | 50 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP] |
[STEP] 2. That's our answer. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP]
[STEP] 2. That's our answer. [/STEP] |
[STEP] 3. Yeah. [/STEP] | 0 | 0 | 5,235 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect th... | 51 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP]
[STEP] 2. That's our answer. [/STEP] |
[STEP] 3. Yeah. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP]
[STEP] 2. That's our answer. [/STEP]
[STEP] 3. Yeah. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,235 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect th... | 52 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP]
[STEP] 2. That's our answer. [/STEP]
[STEP] 3. Yeah. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect that over $y=x$, we get $(-5,6)$. [/STEP]
[STEP] 2. That's our answer. [/STEP]
[STEP] 3. Yeah. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,235 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. Right. If we reflect th... | 53 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP] | 0 | 0 | 5,236 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which m... | 54 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP] |
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP] |
[STEP] 2. I can check by graphing the points and seeing that the line $y=x$ is the perpendicular bisector of the segment joining them. [/STEP] | 0 | 0 | 5,236 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which m... | 55 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP] |
[STEP] 2. I can check by graphing the points and seeing that the line $y=x$ is the perpendicular bisector of the segment joining them. [/STEP] |
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP]
[STEP] 2. I can check by graphing the points and seeing that th... |
[STEP] 3. The final answer is $(-5,6)$. [/STEP] | 0 | 0 | 5,236 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which m... | 56 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP]
[STEP] 2. I can check by graphing the points and seeing that th... |
[STEP] 3. The final answer is $(-5,6)$. [/STEP] |
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP]
[STEP] 2. I can check by graphing the points and seeing that th... |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,236 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which m... | 57 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP]
[STEP] 2. I can check by graphing the points and seeing that th... |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which means swapping the $x$ and $y$ coordinates. [/STEP]
[STEP] 1. The original coordinates are $(6,-5)$, so the reflected coordinates are $(-5,6)$. [/STEP]
[STEP] 2. I can check by graphing the points and seeing that th... | null | 1 | 0 | 5,236 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. I need to reflect the coordinates of the center of the circle across the line $y=x$, which m... | 58 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] | 0 | 0 | 5,237 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 59 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] | 0 | 0 | 5,237 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 60 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] | 0 | 0 | 5,237 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 61 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP]
[STEP] # Answer
-5 [/ST... | null | 1 | 0 | 5,237 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 62 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] | 0 | 0 | 5,238 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 63 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] | 0 | 0 | 5,238 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 64 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 3. Exactly. [/STEP] | 0 | 0 | 5,238 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 65 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 3. Exactly. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,238 | 3 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 66 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,238 | 4 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 67 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP] |
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP] |
[STEP] 1. So the center of the image circle has coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,239 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/... | 68 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP] |
[STEP] 1. So the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP]
[STEP] 1. So the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,239 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/... | 69 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP]
[STEP] 1. So the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/STEP]
[STEP] 1. So the center of the image circle has coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,239 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point $(x,y)$ about the line $y=x$, we swap its coordinates and get $(y,x)$. [/... | 70 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle has coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,240 | 0 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 71 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] | 0 | 0 | 5,240 | 1 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 72 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle has coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle has coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5, 6 [/STEP] | null | 1 | 0 | 5,240 | 2 | 0 | 0 | true | 0 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 73 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP] |
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP] |
[STEP] 2. Thus, the center of the image circle has coordinates $\boxed{(-5,6)}$. [/STEP] | 0 | 0 | 5,241 | 0 | 0 | 0 | true | 0.81 | true | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/ST... | 74 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP] |
[STEP] 2. Thus, the center of the image circle has coordinates $\boxed{(-5,6)}$. [/STEP] |
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP]
[STEP] 2. Thus, the center of the image circle has coordinates $\boxed{(-5,6)}$. [/STEP] |
[STEP] # Answer
$\boxed{(-5,6)}$ [/STEP] | 0 | 0 | 5,241 | 1 | 0 | 0 | true | 0.9 | true | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/ST... | 75 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
|
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP]
[STEP] 2. Thus, the center of the image circle has coordinates $\boxed{(-5,6)}$. [/STEP] |
[STEP] # Answer
$\boxed{(-5,6)}$ [/STEP] |
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/STEP]
[STEP] 2. Thus, the center of the image circle has coordinates $\boxed{(-5,6)}$. [/STEP]
[STEP] # Answer
$\boxed{(-5,6)}$ [/STEP] | null | 1 | 0 | 5,241 | 2 | 1 | 1 | true | 1 | true | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 1. We reflect the center across the line $y=x$ by switching the coordinates of the center. [/ST... | 76 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] | 0 | 0 | 5,237 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 59 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] | 0 | 0 | 5,237 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 60 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] | 0 | 0 | 5,237 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 61 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to switch its $x$ and $y$ coordinates... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP]
[STEP] # Answer
-5 [/ST... | null | 1 | 0 | 5,237 | 3 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 62 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] | 0 | 0 | 5,234 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 46 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,234 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 47 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, the center of the image circle will have coordinates $(-5,6)$. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,234 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 48 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] | 0 | 0 | 5,237 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 59 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] | 0 | 0 | 5,237 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 60 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP] |
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] | 0 | 0 | 5,237 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 61 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP] |
[STEP] # Answer
-5 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the original center is $(6,-5)$, the reflected center will be $(-5,6)$. [/STEP]
[STEP] 2. That means the $x$ coordinate of the center of the image circle is $-5$. [/STEP]
[STEP] # Answer
-5 [/ST... | null | 1 | 0 | 5,237 | 3 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 62 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] | 0 | 0 | 5,232 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 37 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] | 0 | 0 | 5,232 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 38 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP] |
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,232 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 39 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the image is $(-5,6)$. [/STEP]
[STEP] 2. So the x-coordinate of the center of the circle is -5, and the y-coordinate is 6. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,232 | 3 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means that the ima... | 40 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] | 0 | 0 | 5,238 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] | 63 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP] |
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] | 0 | 0 | 5,238 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 64 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP] |
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 3. Exactly. [/STEP] | 0 | 0 | 5,238 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 65 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP] |
[STEP] 3. Exactly. [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] | 0 | 0 | 5,238 | 3 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 66 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP] |
[STEP] # Answer
-5,6 [/STEP] |
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center of the reflected circle will be $(-5,6)$. [/STEP]
[STEP] 2. So the new coordinates of the center of the circle are $-5,6$. [/STEP]
[STEP] 3. Exactly. [/STEP]
[STEP] # Answer
-5,6 [/STEP] | null | 1 | 0 | 5,238 | 4 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. That means the center o... | 67 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] | 0 | 0 | 5,231 | 0 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] | 34 | |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP] |
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] | 0 | 0 | 5,231 | 1 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 35 |
[TURN] # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. So the center of the original circle is $(6,-5)$. [/STEP]
[STEP] 1. When we reflect ... |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP] |
[STEP] # Answer
-5, 6 [/STEP] |
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]
[STEP] 1. So, if the center of the original circle is $(6,-5)$, the center of the image circle is $(-5,6)$. [/STEP]
[STEP] # Answer
-5, 6 [/STEP] | null | 1 | 0 | 5,231 | 2 | 0 | 0 | true | 1 | false | # Question
The center of a circle has coordinates $(6,-5)$. The circle is reflected about the line $y=x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ coordinate first.
# Solution
[STEP] 0. To reflect a point about the line $y=x$, I need to swap its $x$ and $y$ coordinates. [/STEP]... | 36 |
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