# 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

##### 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.

**2**along the x-axis and

**3**up the y-axis. Therefore its Cartesian coordinates are

**(2,3)**