Matrix Transformations (AQA GCSE Further Maths)

Here are two transformations.

A    Rotation clockwise about the origin.
B    Reflection in the line

Use matrix multiplication to work out the single matrix which represents the combined transformation A followed by
B.

The transformation matrix  maps the point onto the point

Work out the values of  and .

You must show your working.

..........................   ..........................

Use matrix multiplication to show that, in the  plane,

• a reflection in the line , followed by

• a rotation, anticlockwise about the origin, followed by

• a reflection in the -axis

is equivalent to a transformation by the identity matrix.

The transformation matrix maps the point onto the point

Work out the values of and .

Use matrix multiplication to show that, in the  plane,

• a reflection in the line , followed by

• a rotation of anticlockwise, centre the origin,

is equivalent to a single transformation, which you should describe.

Under the transformation represented by ,

the image of point is point .

Can point be the same as point ?

You must show your working.

Shape maps to shape by an enlargement, scale factor , centre the origin.

Shape maps to shape by a rotation through , centre the origin.

Shape can be mapped to shape by a single transformation.

Use matrices to show that the single transformation is an enlargement, centre the origin.

State the scale factor of the enlargement.

Use matrices to prove that

a reflection in the line followed by a rotation of anticlockwise about the origin

is not the same as

a rotation of anticlockwise about the origin followed by a reflection in the line

In each case, state the single transformation that they represent.