# Worksheet: Properties of Linear Transformations

Q1:

Consider the matrix where .

Find .

• A
• B
• C
• D
• E

Find .

• A0
• B2
• C
• D
• E1

By drawing the image of the unit square under the transformation, identify the geometrical transformation this matrix corresponds to.

• Ba reflection in the line
• Ca reflection in the line
• Da projection onto the line
• Ea rotation of clockwise about the origin

Q2:

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
• Ban arrowhead with vertices , and
• Ca square with vertices , , , and
• Dan arrowhead with vertices , and
• Ea square with vertices , , , and

What geometric transformation does this matrix represent?

• Aa rotation about the origin by an angle of
• Ba stretch in the -direction
• Ca dilation with scale factor and center the origin
• Da stretch in the -direction
• Ea dilation with scale factor 3 and center the origin

Q3:

The vertex matrix of a square of side 1 shown is

Determine the vertex matrix of the image after a transformation by the matrix , and state what geometric figure it is.

• A, a parallelogram
• B, a rhombus
• C, a square
• D, a rectangle