How to Describe a Rotation

Describing a Rotation

A shape can be rotated. Every point on the shape is turned by an angle about a center of rotation.

To describe a rotation, we need to say what angle the shape has been turned by and where the center of rotation is.

The Center of Rotation

The center of rotation is the point that a shape rotates about.

The image below shows a shape rotated about the center 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 counter-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 center of rotation.

In our example, the Cartesian coordinates of the center 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).

Slider

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

Open the slider in a new tab

See Also

What is geometry? What are transformations? What is an angle? What is are Cartesian coordinates? What is are degrees? What is an angle?