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 anticlockwise) 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.StepbyStep:
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).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 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.