Library/Geometry/Plane geometry/Plane transformations/Movements/Rotation/Rotation (other)

Rotation (other)

Overview
Important

A rotation is a transformation that turns every point of a figure around a fixed point (the center of rotation) by a certain angle. In 'other' contexts, rotations may refer to rotations about points other than the origin, or to rotations in coordinate systems that are not standard, or even to rotations in the complex plane.

Important properties

  • A rotation preserves distances and angles (it is an isometry).

  • The center of rotation can be any point in the plane, not just the origin.

  • The direction of rotation (clockwise or counterclockwise) matters.

  • A rotation by 360° (or 0°) leaves every point unchanged.

  • Composing two rotations with the same center results in another rotation with that center (angle adds up).