12.3 Transforming Shapes

​You can use a combination of reflections, translations and rotations to transform a shape.

You can also describe the transformation that maps an object onto its image.​

​

To describe a reflection you must give:

• the equation of the mirror line​

​To describe a translation you must give:

• the column vector​​

​To describe a rotation you must give:

• the center of rotation

• the number of degrees of the rotation (or fraction of a whole turn)

• the direction of the rotation (clockwise or anticlockwise).​

Note that when a rotation is 180° (half a turn) you do not need to give the direction of the rotation as the image of the object will be the same whether you rotate it clockwise or anticlockwise.​

Worked example a)

The diagram shows triangles A, B, C and D.

a) Draw the image of triangle A after a reflection

in the y-axis followed by a rotation 90° clockwise,

center (−1, 1). Label the image E.

Worked solution a)

First, reflect triangle A in the y-axis to give the blue triangle shown on the diagram. Then rotate the blue triangle 90° clockwise about (−1, 1), shown by a red dot, to give the red triangle.

Remember to label the final triangle E.

Worked example b)

b) Describe the transformations that transform:

i) triangle A to triangle B

ii) triangle B to triangle C

iii) triangle C to triangle D.​

Worked solution b)