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:Top Tip
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.
Note
Clockwise and CounterClockwise
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 counterclockwise or anticlockwise.
A Rotation Can Be Described as Both Clockwise and CounterClockwise
Any rotation can be described as both clockwise and clockwise. The rotation below can be described as both 90° clockwise and 270° counterclockwise:If a rotation is θ clockwise, it is 360 − θ counterclockwise.