A rotation is a transformation in which a figure is turned about a fixed point $P.$ The number of degrees the figure rotates ${\alpha }^{\circ }$ is the angle of rotation. The fixed point $P$ is called the center of rotation. Rotations map every point $A$ in the plane to its image $A^{\prime }$ such that one of the following statements is satisfied.

• If $A$ is the center of rotation, then $A$ and $A^{\prime }$ are the same point.
• If $A$ is not the center of rotation, then $A$ and $A^{\prime }$ are equidistant from $P$, with $\angle AP{A}^{\prime }$ measuring ${\alpha }^{\circ }.$

Rotations are usually performed counterclockwise unless stated otherwise. Notice that a $90^{\circ }$ counterclockwise rotation is the same as a $270^{\circ }$ clockwise rotation. Since rotations preserve side lengths and angle measures, they are rigid motions.