WTMaths logo
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?

Combined transformation question

Combined transformation answer

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?

Translation then a rotation question

translation then a rotation answer

Answer: A rotation, anticlockwise about (-7, 5)