# Rotations of 90°, 180°, 270° and 360° About the Origin (Mathematics Lesson)

# Common Rotations

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:Read more about a 90° rotation about the origin

# A Rotation of 180° About the Origin

The shape below has been rotated 180° (one half turn) clockwise about the origin:Read more about a 180° rotation about the origin

# A Rotation of 270° About the Origin

The shape below has been rotated 270° (three quarter turns) clockwise about the origin:Read more about a 270° rotation about the origin

# A Rotation of 360° About the Origin

The shape below has been rotated 360° (one whole turn) clockwise about the origin:Read more about a 360° rotation about the origin

##### Curriculum

##### Interactive Test

**show**

##### 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

**WHAT IS A ROTATION?**

A rotation turns a shape around a center.

A rotation is a type of transformation.

**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.