Combination of Transformations

Combination of Transformations

GCSE(H),

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.

Examples

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

2. Shape A is rotated 90º anticlockwise with a centre of rotation (-1, 3) to map onto shape B. Shape B is then rotated 90º clockwise wit ha centre of rotation (-4, 6) to map onto shape C. What single transformation maps shape A onto shape C?

Answer: A translation, with vector ((-6),(0))