# Rotation

**Describing a rotation**

**Rotation** is defined as when an object is turned around a fixed point. The following points should be know when describing a rotation:

- The
**angle**(e.g. ½ turn = 180°, ¾ turn = 270°) - The
**direction**(e.g clockwise or anticlockwise) - The
**centre**(this is the fixed point where an object moves)

**Rotating shapes**

If triangle ABC is rotated 90° clockwise from point O the following **image** is produced:

The image is therefore **congruent** from triangle A’B’C’ to triangle ABC.

Point to note: The centre of rotation can also be inside the shape.

**Determining the direction of a rotation**

The rotation of the direction can be described as:

**P****ositive**rotation is**anticlockwise****N****egative**rotation is**clockwise**

Therefore

60° rotation = anticlockwise rotation of 60°

–90° rotation = clockwise rotation of 90°

**Inverse rotations**

An image that has been rotated back onto the original object is called the invert of a rotation. This can be either:

- rotation of the
*same*size, about the same point and in the*opposite*direction,**or** - rotation in the
*same*direction, about the same point, but the two rotations have a sum of 360°

**Finding the centre of rotation**

To find the centre of a rotation, the following steps are taken:

- Draw lines from any two vertices to the images
- Mark the mid-point of each line
- Draw perpendicular lines from each of the mid-points
- The point where these lines meet is the centre of rotation

**Finding the angle of rotation**

To find the angle of rotation, the following steps are taken:

- Find the centre of the rotation and join one vertex and its image to it
- Use a protractor to measure the angle of rotation