Geometry (all content)
An older video where Sal finds the images of shapes under various rotations, and where he determines the rotations that take one shape to another. Created by Sal Khan.
What is the image of the polygon below after the rotation? So this is a rotational transformation of 270 degrees. So what we-- and when they talk about a rotational transformation, at least in the context of this exercise, we're talking about a rotation around the origin, so around this point. So the way I like to think about it is pick one of these points, one of these orange points, and, essentially, rotate it around the origin 270 degrees. So let's do that. So this would be rotating it. And when we talk about positive angles, we're talking about going in the counterclockwise directions. The same way that we, typically, measure angles when we're doing trigonometry with the unit circle and things like that. So here, so we started here, and let's rotate 90 degrees. Then we could keep rotating, rotate another 90 degrees so we've rotated a total of 180 degrees. And then we rotate 90 more degrees to get to 270. Let's do a couple more of these. What is the transformation that rotates the blue solid shape to the orange dashed shape? Now, this one's a little bit-- we don't have the manipulative here to help us answer that question so this is really going to challenge our powers of visualization. So the main thing is to pick a point on the blue shape and see where does it end up on the orange dashed shape. And I'll pick this point right over here because you can see it's pointing straight to the top left. And then when you go onto the orange dashed shape, it's pointing to the bottom right. So this one went all the way around. So you could say it went-- it was pointing from this direction and went all the way to going in the exact opposite direction. So this was a 180-degree transformation, a 180-degree rotation. Let's do a few more. So what's the image of the polygon? So they want us to do another 270-degree rotation. So like before. So let's rotate this 3/4 of the way around. So let's see how we can do that. So right now-- so this is going to be a little bit trickier. So if we-- actually, I'm going to pick this point because it's easier to visualize the 270 degrees. So now we've done 90 degrees. Now we can do 180 degrees. And now we've done 270 degrees.