Main content

## Geometry (all content)

### Unit 10: Lesson 9

Old transformations videos# Rotation examples (old)

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.

## Video transcript

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.