Matrix Transformations (AQA GCSE Further Maths)

The transformation matrix maps the point (3, 4) onto the point (8, −7)

Work out the values of and .

[5]

Here are two transformations.

A    Rotation 90° 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.

[4]

The transformation matrix  maps the point (1, −3) onto the point (1, 4)

Work out the values of  and .

You must show your working.

..........................   ..........................[5]

Use matrix multiplication to show that, in the  plane,

• a reflection in the line , followed by
• a rotation, 90° anticlockwise about the origin, followed by
• a reflection in the -axis

is equivalent to a transformation by the identity matrix.

[5]

Under the transformation represented by ,

the image of point is point .

Can point be the same as point ?
You must show your working.

[4]

Shape maps to shape by an enlargement, scale factor 3, centre the origin.

Shape maps to shape by a rotation through 180°, centre the origin.

Shape can be mapped to shape C 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.

[5]