Combination of Transformations

## Combination of Transformations

One transformation can be followed by one or more further transformations.

The resultant transformation may be mappable by a single transformation.

Some transformations are readily combined: for example, a translation followed by a further translation can be replaced by a single translation (the single translation is called the resultant vector); and a reflection in one axis followed by a reflection in the other axis has the same effect as a rotation.

## Example 1

Shape A is reflected in x = 0 to map to shape B. Shape B is then reflected in y = 0 to map to shape C.

What single transformation would map shape A onto shape C?

Answer: A rotation of 180º around the origin

## Example 2

Shape A is translated using a vector of ((-6),(0)) onto shape B.

Shape B is then rotated anticlockwise by 90º.

What single transformation maps shape A onto shape C?