In this section we combine transformations. We see that sometimes 2 transformations are equivalent to a single transformation.

Here we use transformations from the following types:

Translations | Enlargements | Reflections | Rotations |

The shape shown in the diagram is reflected first in the y-axis and its image is then reflected in the x-axis.

What single transformation would have the same result as these two transformations?

The diagram shows how the original shape A is first reflected to B, and B is then reflected to C.

A rotation of 180° about the origin would take A straight to C.

A triangle is to be enlarged with scale factor 2, using the origin as the centre of enlargement. Its image is then to be translated along the vector .

The coordinates of the corners of the triangle are (2, 1), (2, 4) and (4, 1).

What *single* transformation would have the same result?

The diagram shows the original triangle, A; the enlargement takes it to B, which is then translated to C.

The triangle A could be enlarged with scale factor 2 to give C.

This diagram shows that the centre of enlargement would be the point

The single transformation that will move triangle A to triangle C is an enlargement, scale factor 2, centre