Rotation of $90^\circ$

A 90^0 rotation about a point $O$ moves every point $P$ in the plane to a new point $P'$ such that the distance $OP = OP'$ and the angle $POP'$ is 90^0, measured in the chosen direction (clockwise or counterclockwise). In coordinates, rotating a point $(x, y)$ about the origin by 90^0 counterclockwise gives $(-y, x)$; clockwise gives $(y, -x)$.

Important properties

• A 90^0 rotation preserves distances and angles (it is an isometry).

• Four 90^0 rotations (in the same direction) return a figure to its original position.

• The orientation of the figure changes with each 90^0 rotation.