The Lesson

A shape can be rotated. Every point on the shape is turned by an angle about a centre of rotation. To describe a rotation, we need to say what angle the shape has been turned by and where the centre of rotation is.

The Centre of Rotation

The centre of rotation is the point that a shape rotates about. The image below shows a shape rotated about the centre of rotation with Cartesian coordinates (3, 3).

The Angle of Rotation

The angle of rotation is the angle that the shape has been rotated about. It can be described in degrees or radians. The direction of the rotation (clockwise or anti-clockwise) can also be described. The image below shows a shape rotated by an angle of 120° clockwise.

How to Describe a Rotation

Describing a rotation is easy.

Question

Describe the rotation shown below.

Step-by-Step:

1

Find the centre of rotation. In our example, the Cartesian coordinates of the centre of rotation is (1, 1).

2

Using a protractor or otherwise, find the angle the shape has been rotated. The angle is 60° clockwise.

Answer:

The light blue shape has been rotated 60° about (1, 1).

Lesson Slides

The slider below shows another real example of how to rotate a shape.

Top Tip

How to Think of the Center of Rotation

Imagine a shape is drawn on a sheet of paper...Imagine sticking a pin through the paper 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.The pin would be the center of rotation.

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.