In this worksheet, we will practice finding the matrix representation of dilations as geometric linear transformations.

**Q1: **

Consider the transformation represented by the matrix

What is the image of the square with vertices , , , and under this transformation?

- Aa kite with vertices , and
- Ba kite with vertices , and
- Ca square with vertices , , , and
- Da square with vertices , , , and
- Ea square with vertices , , , and

What geometric transformation does this matrix represent?

- Aa dilation with scale factor 3 and centre the origin
- Ba rotation about the origin by an angle of
- Ca stretch in the -direction
- Da stretch in the -direction
- Ea dilation by a factor of 3 with its centre at the point

**Q2: **

Describe the geometric effect of the transformation produced by the matrix .

- Aa dilation with centre the origin and scale factor 3 followed by a rotation about the origin
- Ba dilation with centre the origin and scale factor 3 followed by a reflection in the line
- Ca dilation with centre the origin and scale factor 3 followed by a reflection in the line
- Da dilation with centre the origin and scale factor 3 followed by a rotation about the origin
- Ea dilation with centre the origin and scale factor 3 followed by a rotation about the origin

**Q3: **

Which of the following compositions of transformations is represented by the matrix ?

- Aa dilation with centre the origin and scale factor 2 followed by a reflection in the line
- Ba dilation with centre the origin and scale factor followed by a reflection in the line
- C a dilation with centre the origin and scale factor 2 followed by a reflection in the line
- Da dilation with centre the origin and scale factor followed by a reflection in the line
- Ea rotation by about the origin followed by a reflection in the line

**Q4: **

A dilation with center the origin is composed with a rotation about the origin to form a new linear transformation. The transformation formed sends the vector to .

Find the matrix representation of the transformation formed.

- A
- B
- C
- D
- E

Find the scale factor of the original dilation.

- Ascale factor = 13
- Bscale factor =
- Cscale factor = 154
- Dscale factor = 169
- Escale factor = 13

**Q5: **

The unit square, with vertices , and , is transformed by a rotation and then a dilation. Its image under this combined transformation is , as shown in the diagram.

What are the coordinates of ?

- A
- B
- C
- D
- E

What is the matrix of the combined transformation?

- A
- B
- C
- D
- E