## The Lesson

A rotation can be by any angle about any center of rotation. However, it can be time consuming to rotate a shape and even more difficult to describe a rotation. Rotations of 90°, 180°, 270° and 360° about the origin, however, are relatively simple.

## A Rotation of 90° About the Origin

The shape below has been rotated 90° (one quarter turn) clockwise about the origin: ## A Rotation of 180° About the Origin

The shape below has been rotated 180° (one half turn) clockwise about the origin: ## A Rotation of 270° About the Origin

The shape below has been rotated 270° (three quarter turns) clockwise about the origin: ## A Rotation of 360° About the Origin

The shape below has been rotated 360° (one whole turn) clockwise about the origin: ## How to Think of Rotations About the Origin

Imagine a shape is drawn on a pair of axes on a sheet of paper... Imagine sticking a pin through the origin and into a surface... If you span the paper around, the pin would stay in place and every other point on the paper would turn in a circle around it. By turning the paper in a series of one... two... three... four quarter turns, the rotations described on this page can be found. ## Clockwise and Counter-Clockwise

The direction of rotation is needed to describe a rotation.
• If the rotation is in the same direction as the hands of a clock, the direction is clockwise. • If the rotation is in the opposite direction as the hands of a clock, the direction is counter-clockwise or anti-clockwise. ## A Rotation Can Be Described as Both Clockwise and Counter-Clockwise

Any rotation can be described as both clockwise and clockwise. The rotation below can be described as both 90° clockwise and 270° counter-clockwise: If a rotation is θ clockwise, it is 360 − θ counter-clockwise.