A rotation is a transformation in which a figure is turned about a fixed pointP by a certain angle measure α∘. The point P is called the center of rotation. Rotations map every point A in the plane to its imageA′ such that one of the following statements is satisfied.
If A is the center of rotation, then A and A′ are the same point.
If A is not the center of rotation, then A and A′ are the same distance from P, and ∠APA′ has a measure of α∘.
The angle formed by a preimage, the center of rotation, and the image is called the angle of rotation and its measure is α∘. Since rotations preserve side lengths and angle measures, they are rigid motions.
Usually, rotations are performed counterclockwise unless otherwise stated.