standard_description: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
problem_activity: Problem 1
Figure 1 (F1) and Figure 2 (F2) are shown below. For each statement below, determine if it is true or false. Explain your reasoning.
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a.   A reflection over the
$$x$$
-axis and a translation to the left will transform F1 to F2, making the two figures congruent.
b.   A rotation of
$${180^{\circ}}$$
about the origin will transform F1 to F2, making the two figures congruent.
c.   A dilation from the origin and a translation up will transform F1 to F2, making the two figures similar.
d.   A reflection across the
$$x$$
-axis and a reflection across the
$$y$$
-axis will transform F1 to F2, making the two figures congruent.
e.   There is no sequence that will transform Figure 1 to Figure 2, making the two figures neither congruent nor similar.
Problem 2
The pentagon shown below is the resulting image of pentagon
$${ABCDE}$$
after it was dilated from point
$$A$$
by a scale factor of
$${\frac{1}{2}}$$
and then rotated clockwise
$${90^{\circ}}$$
about point
$$A$$
.
What are the original coordinates of pentagon
$${ABCDE}$$
?
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aligns: no