Let’s start by looking at rotating a point about the center \((0,0)\). Here is a figure rotated 90° clockwise and counterclockwise about a center point.Ī great math tool that we use to show rotations is the coordinate grid. We specify the degree measure and direction of a rotation. The angle of rotation is usually measured in degrees. The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. Another great example of rotation in real life is a Ferris Wheel where the center hub is the center of rotation. A figure can be rotated clockwise or counterclockwise. A figure and its rotation maintain the same shape and size but will be facing a different direction. We call this point the center of rotation. More formally speaking, a rotation is a form of transformation that turns a figure about a point. There are other forms of rotation that are less than a full 360° rotation, like a character or an object being rotated in a video game. The wheel on a car or a bicycle rotates about the center bolt. The earth is the most common example, rotating about an axis. So this is definitely a dilation, where you are, your center where everything is expanding from, is just outside of our trapezoid A.Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point. 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. Has it been translated? And the key here to realize is around, what is your center of dilation? So for example, if yourĬenter of dilation is, let's say, right over here, then all of these things are Now you might be saying, well, wouldn't that be, it looks like if you're making somethingīigger or smaller, that looks like a dilation. The distance between corresponding points looks like it has increased. Get to quadrilateral B? All right, so this looks like, so quadrilateral B is clearly bigger. What single transformation was applied to quadrilateral A to So it's pretty clear that this right over here is a reflection. This got flipped over the line, that got flipped over the line, and that got flipped over the line. Some type of a mirror right over here, they'reĪctually mirror images. And then this pointĬorresponds to that point, and that point corresponds to that point, so they actually look like Get to quadrilateral B? So let's see, it looks like this point corresponds to that point. And I don't know the exact point that we're rotating around,īut this looks pretty clear, like a rotation. And if you rotate around that point, you could get to a situation This point went over here, and so we could be rotating around some point right about here. Looks like there might be a rotation here. Translated in different ways, so it's definitely notĪ straight translation. So it doesn't look likeĪ straight translation because they would have been What single transformation was applied to triangle A to get to triangle B? So if I look at these diagrams, this point seems toĬorrespond with that one. And so, right like this, they have all been translated. Or another way I could say it, they have all been translated a little bit to the right and up. Happened is that every one of these points has been shifted. What single transformation was applied to triangle A to get triangle B? So it looks like triangleĪ and triangle B, they're the same size, and what's really So with that out of the way, let's think about this question. Going to either shrink or expand some type of a figure. And we'll look at dilations, where you're essentially We're gonna look at reflection, where you flip a figure We're gonna look at translations, where you're shifting all Where you are spinning something around a point. We're gonna look at are things like rotations Going to do in this video is get some practice identifying
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