Okay, welcome back to Extra Help from Mr. A and today I'm going to be teaching you a little bit about transformational geometry. First thing we're going to do is we are going to take a look at translations. So when I do a translation, I find it a lot easier to move point by point rather than moving the entire shape. So over here we see our transformation that we want to do which is a translation. And here's our original figure. It's labeled ABCD. So rather than try to think of this as moving up polygon like this, what I'm going to do is I'm going to move each point according to this criteria. So for my A point I'm going to go 1, 2, 3, right, 1, 2 down. And this is going to be my new A point. I'm going to put a little apostrophe beside it and call it A-prime. That's to show that it's an image and not the original figure. Next I'm going to do the same thing with my B point. I'm going to take my B and I'm going to move it to three spaces right and then two spaces down. 1, 2, 3, 1, 2. This is my new B point and again I'll call this B-prime to show that it's an image not the original figure. Same thing with our C. 1, 2, 3, 1, 2. Here's our C point, C-prime, and then D, 1, 2, 3, 1, 2. And this is D-prime. Then it's just simply a matter of connecting the dots using a straight edge so that you don't lose points. What a silly reason to lose points. Then we get the exact proportions of one side to another here. That was supposed to be getting. I'll make this my D-prime. And it's really easy if you do a point by point. That's the reason I enjoyed doing it point by point rather than moving the whole figure. So I'm going to do a lot more simple and you're able to make sure that the lines are in proportion to one another. Now I have added a reflection line here called reflection line L. I made it a cursive L because a regular lowercase L would just look like a 1. That's why we use cursive L when we're doing math. So my reflection line, again, it's a lot simpler to do at point by point rather than trying to move the whole figure at once. So all I'm going to do is I'm going to count how far away these points are from my reflection line and then I'm just going to do the opposite on the other side. So let's start with C because this is the closest to the reflection line. It is 1 block away from the reflection line. So it's 1 block above. So on our reflection line it should be 1 block below. So put a little dot here. This will be my C prime prime because this is the second time I've done a transformation to this image. Now we'll do our D point. So D is two points above or sorry two blocks above the reflection line. So D prime prime should be two blocks below. Next we'll do A. A is 1 to 3 above. And A prime prime will be 1 to 3 below. It will be right on our x axis here. And then finally B is also 3 away. 1 to 3 above. So it should be 1 to 3 down. So B prime prime. And again take out your straight edge. Connect the dots as we all did in kindergarten. And you will have for yourself a squeaky door and a perfect reflection of your image. So again my advice for you for transformations particularly translations and reflections is to do it point by point rather than thinking of it as an entire polygon. If you do a point by point it's a lot simpler. We will do rotations in just a moment. So now I'm going to explain how to do a rotation. The first thing you need to be aware of with rotations is how to interpret the instructions. Generally with rotational instructions you're going to be given a degree. So how far the rotation is going to go. A direction which is clockwise or counterclockwise and I've made a little note there. And then it's going to say about. And what the word about means in this context is where is the center of your rotation. In other words if you are playing a record where would that center of that record be. If you're talking about a donut it would be where is the hole basically. And then it's going to give you a point which will be the center of your rotation. So if I go to 4,5 which is right here. This dot right here is the center of my rotation. So we're rotating this figure 90 degrees clockwise about 4,5. It does really make a difference where your center of your rotation is. Depending on how far away your figure is from the center of rotation. It's going to throw it into different locations. So you really need to make sure. The first method I'm going to show you how to do with the rotation is using good old fashioned tracing paper. So what you do is you pop your tracing paper down. And I don't even bother copying the whole figure. I just copy the points. So I'm copying the vertices of this polygon. And I'm going to label them as they are labeled on the original sheet. So those are the vertices of my polygon. So now what I'm going to do is I'm going to take my pen and I'm going to put it down at the center of my rotation. Which is 4,5. Put it there and hold it. And then I'm going to rotate my tracing paper 90 degrees. Now if this helps you can also put an arrow pointing straight up on your sheet. Okay, that would be 12 o'clock right now. We want to rotate it so it would be pointing at 3 o'clock. Because that would be 90 degrees clockwise. So I'm going to twist this paper so that my arrow is pointing directly horizontally. And we see our new points. This is where the rotation would end up. For A or A prime, what I'm going to do is I'm going to copy down his coordinates on this sheet. Because it's really difficult to lift your paper and put down the points. I prefer to write the coordinates onto my sheet. So A is now at 7,7. B is at 7,6. C is at 5,6. And D is at 6,7. And then all you have to do is take these coordinates. And essentially just pop them onto your grid. There's another way of doing it as well. If you don't want to go to all the tracing it on the tracing paper. This way is effective for some people. Just like tracing paper is effective for some people. Some people can go between the ways equally well and some can't. It's all up to you and what you find useful. So what I'm going to do is around the center of rotation I'm going to draw a little grid. Or sorry, I'm going to draw a cross here. And what I'm going to do as the image sharpens here. I'm going to measure how far, well, each point is away from the center of rotation. So this is my baseline right here that I'm going to be using almost like a measuring tool. And I'm going to use this line as a reference. And I can imagine this line rotating up to being this vertical line. I know that doesn't really make too much sense. And again, this method might not work for everybody. What I'm going to do is I'm going to count how far away it is from the center. So we go one over and one up. Okay. If we are rotating this, then we should go one up and one over. So my new C location is right here. I'll call this C prime. D is one two, sorry, two over and two up. So it'll be two up and two over. That's D prime. A is two over and three up. So two over and three over. Sorry, two up and three over. And then finally B is one over and three up. So we'll go one up and three over. And you will notice that this figure is exactly the same place as we would expect it to be when we use the tracing paper. Some methods are easier than others. And again, it makes sense sometimes for some people to use one method and another method another time. And some people will never get this method. And that's absolutely fine because we have the tracing paper which helps us. Just to prove that these two figures are the same thing, I'm going to take my tracing paper again. And hopefully the vertices of the tracing paper will line up with my new image. And indeed they do. So both ways I got the correct rotation. Okay. One way I used tracing paper the other way I did. Thank you.