Finding the image of a point under a rotation. The example includes positive and negative angles of rotation.
- [Instructor] We're told that point P was rotated about the origin (0,0) by 60 degrees. Which point is the image of P? Pause this video and see if you can figure that out. All right, now let's think about it. This is point P. It's being rotated around the origin (0,0) by 60 degrees. So if originally point P is right over here and we're rotating by positive 60 degrees, so that means we go counter clockwise by 60 degrees. So this looks like about 60 degrees right over here. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. So does this look like 1/3 of 180 degrees? Remember, 180 degrees would be almost a full line. So that indeed does look like 1/3 of 180 degrees, 60 degrees, it gets us to point C. And it looks like it's the same distance from the origin. We have just rotated by 60 degrees. Point D looks like it's more than 60 degree rotation, so I won't go with that one. All right, let's do one more of these. So we're told point P was rotated by negative 90 degrees. The center of rotation is indicated. Which point is the image of P? So once again, pause this video and try to think about it. All right, so we have our center of rotation, this is our point P, and we're rotating by negative 90 degrees. So this means we are going clockwise. So we're going in that direction. And 90 degrees is easy to spot. It's a right angle. And so it would look like that and it looks like it is getting us right to point A. So this is a negative 90 degree rotation right over here. Gets us to point A.