# Worksheet: Dilation Transformation Matrix

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