Introduction to rigid transformations
- [Instructor] What we're going to do in this video is get some practice identifying some transformations. And the transformations we're gonna look at are things like rotations where you are spinning something around a point. We're gonna look at translations, where you're shifting all the points of a figure. We're gonna look at reflection, where you flip a figure over some type of a line. And we'll look at dilations, where you're essentially going to either shrink or expand some type of a figure. So with that out of the way, let's think about this question. What single transformation was applied to triangle A to get triangle B? So it looks like triangle A and triangle B, they're the same size, and what's really happened is that every one of these points has been shifted. Or another way I could say it, they have all been translated a little bit to the right and up. And so, right like this, they have all been translated. So this right over here is clearly a translation. Let's do another example. What single transformation was applied to triangle A to get to triangle B? So if I look at these diagrams, this point seems to correspond with that one. This one corresponds with that one. So it doesn't look like a straight translation because they would have been translated in different ways, so it's definitely not a straight translation. Let's think about it. Looks like there might be a rotation here. So maybe it looks like that point went over there. That point went over there. This point went over here, and so we could be rotating around some point right about here. And if you rotate around that point, you could get to a situation that looks like a triangle B. And I don't know the exact point that we're rotating around, but this looks pretty clear, like a rotation. Let's do another example. What single transformation was applied to quadrilateral A to get to quadrilateral B? So let's see, it looks like this point corresponds to that point. And then this point corresponds to that point, and that point corresponds to that point, so they actually look like reflections of each other. If you were to imagine some type of a mirror right over here, they're actually mirror images. This got flipped over the line, that got flipped over the line, and that got flipped over the line. So it's pretty clear that this right over here is a reflection. All right, let's do one more of these. What single transformation was applied to quadrilateral A to get to quadrilateral B? All right, so this looks like, so quadrilateral B is clearly bigger. So this is a non-rigid transformation. The distance between corresponding points looks like it has increased. Now you might be saying, well, wouldn't that be, it looks like if you're making something bigger or smaller, that looks like a dilation. But it looks like this has been moved as well. Has it been translated? And the key here to realize is around, what is your center of dilation? So for example, if your center of dilation is, let's say, right over here, then all of these things are gonna be stretched that way. And so this point might go to there, that point might go over there, this point might go over here, and then that point might go over here. So this is definitely a dilation, where you are, your center where everything is expanding from, is just outside of our trapezoid A.