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Worksheet: Dilation Transformation Matrix
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 center 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 center at the point
Q2:
Describe the geometric effect of the transformation produced by the matrix .
- Aa dilation with center the origin and scale factor 3 followed by a rotation about the origin
- Ba dilation with center the origin and scale factor 3 followed by a reflection in the line
- Ca dilation with center the origin and scale factor 3 followed by a reflection in the line
- Da dilation with center the origin and scale factor 3 followed by a rotation about the origin
- Ea dilation with center the origin and scale factor 3 followed by a rotation about the origin
Q3:
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
Q4:
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
Q5:
Which of the following compositions of transformations is represented by the matrix ?
- Aa dilation with center the origin and scale factor 2 followed by a reflection in the line
- Ba dilation with center the origin and scale factor followed by a reflection in the line
- C a dilation with center the origin and scale factor 2 followed by a reflection in the line
- Da dilation with center 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