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# Mapping shapes

## Video transcript

- [Instructor] So I'm here on the Khan Academy Exercise for mapping shapes. And I'm asked to map the movable quadrilateral onto quadrilateral ABCD using rigid transformations. So here in blue, I have the movable quadrilateral. And I want to map it onto this quadrilateral in gray. And we have a series of tools here rigid transformations of translation, rotation and reflection on the Khan Academy tool. And of course, we can undo it. So the technique I'm going to use to do this is I'm gonna first use translation to make one of the corresponding points overlap with the point that it corresponds to. So, for example, it looks like this corresponds to Point C right over here. And so I am going to translate. And so notice, once I click that I can translate this around. So I'm gonna translate right over here to Point C. And now, let's see. To make these two overlap I really can't do anymore translation, I made one point overlap. Do I rotate, or do I reflect? Well, if I eyeball it right over here it looks like I am doing a rotation. Let me try to make user rotation to make this segment eight over here overlap with segment CD. So let me do a rotation now. And so let's see, yep, this is looking good There you go. We did the rotation and we are done. Now, let's do another example. So, here, what do we need to do? All right, so I'm gonna do the same technique. This seems to correspond to Point C so I'm gonna translate first. So, translate first. And then, there's something interesting going on right over here. Because I've actually been able to overlap points C and A by shifting it. By translating it, I should say. And so it's not clear if I were to rotate it then I would lose the fact that A that the point that corresponds to A is now sitting on top of A. The point that corresponds to C is now sitting on top of C. It feels like a reflection. And it looks like a line that would actually contain the points A and C. If we reflect over that line we will be in good shape. So let me see. Reflection. So let me see, move of the line. See how it looks. There, that's not what I wanted to do. So let's see. Let me move my line. So that is, I think, a good line of reflection. And then let me actually try to reflect, and there you go. I was able to reflect over that line. And my clue that I had to reflect over the line that contained A and C is that the points A and C and their images after the transformation were all sitting on top of each other. So, that was a good clue that on a reflection if they're both sitting on the line of reflection that they wouldn't move, so to speak. And there you have it. So this was a translation and then a reflection.