Follow Us on Twitter

Rotation (Mathematics Lesson)

What Is a Rotation?

In geometry, a rotation turns a shape around a center.

A rotation is a type of transformation.

A Real Example of Rotation



The diagram above shows a triangle before (light blue) and after (dark blue) being rotated.

Properties of Rotation

  • All points move in a circle around the center.


  • Each point in the rotated shape (image) is the same distance from the center as the original shape (object).

  • The image is the same size as the object.

Describing a Rotation

Question: Describe the rotation below.



A rotation is described by the angle of rotation and the center of rotation.

The shape has been rotated θ degrees clockwise about the center of rotation (x, y).

Read more about how to describe a rotation

How to Rotate a Shape

Question: Rotate the shape below by 90° clockwise about the point (3, 2).



Read more about how to rotate a shape
Curriculum
Geometry Lessons
Interactive Test
  show
 
Note

TRANSFORMATIONS

A rotation is a type of transformation.

The other types of transformation are:

ROTATED SHAPES ARE CONGRUENT SHAPES

If a shape can be transformed to another using only rotation, then the two shapes are congruent.

Congruent shapes have the same size, line lengths, angles and areas.

They are the same shape and size, just in a different position.

HOW TO DESCRIBE THE CENTER OF ROTATION

The center of rotation can be described using Cartesian coordinates, (x, y).



  • The coordinate on the left is the x-coordinate.

    It describes how far along the x-axis, or how far across, the point is.

  • The co-ordinate on the right is the y-coordinate.

    It describes how far up the y-axis, or how far up, the point is.
For example, the point below is 2 along the x-axis and 3 up the y-axis. Therefore its Cartesian coordinates are (2,3)