# How to Rotate a Shape (Mathematics Lesson)

# How to Rotate a Shape

To rotate a shape, rotate each point on the shape by the angle of rotation about the center of rotation.Each point on the shape above has been rotated

**θ**degrees clockwise about the center of rotation

**(x, y)**.

# Common Examples of How to Rotate a Shape

Common rotations are rotations of 90°, 180°, 270° and 360° about the origin.It is often possible to rotate these shapes by eye.

Read more about common rotations

# A Real Example of How to Rotate a Shape

It is possible to rotate a shape by any angle about any center of rotation.**Question:**Rotate the shape below by

**60°**clockwise about the point

**(3, 1)**.

**Step 1:**Find the center of rotation.

The center of rotation has Cartesian coordinates (3, 1).

It is 3 units along the x-axis and 1 unit up the y-axis.

For each vertex (corner) of the shape (vertex A in this example).

**Step 2:**Draw a line from the center of rotation to the vertex.

**Step 3:**Measure the angle of rotation from the line.

Using a protractor, find 60° clockwise from the line found.

**Step 4:**Draw a line of the same length as in

**Step 2**from the center of rotation at the angle found in

**Step 3**.

Vertex A has been rotated 60° about (3, 1) to find A', the corresponding point on the rotated shape.

Repeat for vertex B and C:

With all vertices of the shape rotated, the rotate shape can be drawn:

The shape has been rotated 60° clockwise about (3, 1).

##### Curriculum

##### Interactive Test

**show**

##### Note

**WHAT IS A ROTATION?**

A rotation turns a shape around a center.

A rotation is a type of transformation.

# HOW TO DESCRIBE A ROTATION

A rotation is described by the angle the shape turns about a center of rotation.- The
**center of rotation**is the point that a shape rotates about.

It can be described by Cartesian coordinates,**(x, y)**.

The center of rotation may be found by observation or by construction. - 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 counterclockwise) can also be described.

# HOW TO DESCRIBE THE CENTER OF ROTATION

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

- The co-ordinate 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)**

**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**.

##### Top Tip

# HOW TO THINK 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, and the amount you span the paper would be the angle of rotation.