Rotation of Geometric Objects

A rotation is a transformation in which a figure is turned about a fixed point P. The number of degrees the figure rotates α ^(∘) 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' 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 equidistant from P, with ∠ APA' measuring α ^(∘).

Rotations are usually performed counterclockwise unless stated otherwise.

Notice that a 90^(∘) counterclockwise rotation is the same as a 270^(∘) clockwise rotation. Since rotations preserve side lengths and angle measures, they are rigid motions.