About this video
The instructor works out where quadrilateral M lands after a 240-degree clockwise rotation about point R. He draws circles centred at R through M's vertices, since rotated points stay on these circles, which rules out B, then uses benchmarks of 180 and 270 degrees to rule out A and choose C.
You'll be able to
- explain why a rotated point stays on a circle centred at the centre of rotation.
- use benchmark angles (90, 180, 270 degrees) to estimate where a rotated point ends up.
- identify the image of a figure after a given rotation.
Key words
- rotation
- A turn of a figure about a fixed point by a given angle and direction.
- centre of rotation
- The fixed point a figure turns around; here it is point R.
- clockwise
- Turning in the same direction as the hands of a clock.
- radius
- The distance from the centre of a circle to a point on it; a rotated point keeps its distance from R.
Transcript
- [Instructor] We are told Quadrilateral M is rotated 240 degrees clockwise about point R. So, this is Quadrilateral M right over here. This is point R. And what we need to figure out is, after we rotate it, what would it be? Would it be Quadrilateral A, B, or C?
So, pause this video, and have a go at that before we do this together. Okay, so one way to think about this, let's just focus on one of the vertices of Quadrilateral M, and think about what would it look like after a 240-degree rotation. So, one way to think about it, if we have that, think about the distance between that and R.
You could consider that the radius, because we're about to draw a circle. And if you were to rotate it, it would draw out a circular path. And if you were to go all the way over here, that would be... Actually, if you were to go all the way over onto the other side, you would get right around there.
That would be 180 degrees. And then if you were to go further over there, that would get you to 270 degrees, which is a little bit too far. So, this point would rotate someplace around here. Now, to make that very clear what the possible new vertex would be after the rotation, let me see, lemme get the circle tool out here.
And actually, let me draw a perfect circle 'cause I am not so good at drawing a perfect circle. So, I'm gonna draw a perfect circle centered at R and going through that vertex. And there we have it. So, when you look at that, you can see that that corresponding vertex right over here, it could be this one.
That one seems to be right on that circle. And this one also seems to be right on that circle. We don't see anything on Quadrilateral B that sits on that circle. So, I'm gonna rule out Quadrilateral B. There's no corresponding vertex there. And so, between A and C, we just said that if we're rotated 180 degrees, we would get all the way over here.
So, we're going even further than that. So, that would rule out choice A. And so, we can feel pretty good that this is going to be choice C. If we wanna confirm that, we can look at what would happen to all of the other vertices when we rotated. And to do that, I can just try to draw more circles here.
So, let me now draw a circle that captures that vertex right over there. Whoops, that's not how I want. I didn't wanna make it that big. Let's see. Do it like that. All right, right over there. I was just trying to go through this point, and once again, that corresponding point on A and C go through it.
But for A, we're not rotated enough. A could be something that, if you rotate M by some degrees, looks like it's a little over 90 degrees clockwise, you could get to A; but if you're going 240 degrees clockwise, you are getting to C. And once again, B does not have...
This point right over here does not sit on that second circle.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.