We need to be able to recognise what transformation has taken place when we are shown an object and an image. This means finding not just, for example, that a rotation has taken place, but also finding the centre of rotation, the magnitude of the rotation and the direction of the rotation.

Describing Reflections

To find the mirror line, we just need to take the perpendicular bisector of any two corresponding points from the object and the image.

Describing Enlargements

To find the centre of enlargement, we draw lines joining each of the corresponding vertices of the object and the image. Where these lines meet will be the centre. Once we have found the centre, we can easily find the scale factor by dividing the distance from the centre to a vertex of the image by the distance form the centre to a vertex of the object.

Describing Rotations

To find the centre of rotation we again draw lines joining each of the corresponding vertices of the object and the image. We then need to draw perpendicular bisectors of each of these lines. Where these perpendicular bisectors meet will be the centre of rotation. Once we have found the centre of rotation we can easily find the magnitude and the direction of the rotation by drawing lines from the centre to two corresponding vertices and measuring that angle.

Examples

Exercise

Let’s complete exercise 15H from pages 256 and 257 of the textbook;

The answers are below: