**Q1: **

A translation of 3 units right and 2 units down can be described by the vector .

Describe the translation from point to point using a vector.

- A
- B
- C
- D
- E

The point is translated using the vector . What are the coordinates of its image?

- A
- B
- C
- D

**Q2: **

Consider the given figure.

The points , , , and are corners of the unit square. This square is reflected in the line with equation to form the image .

As is the image of in the line through and , . Use this fact and the identity to find the gradient and hence equation of from the gradient of .

- A
- B
- C
- D
- E

Using the fact that is perpendicular to , find the equation of .

- A
- B
- C
- D
- E

Using the fact that , find the coordinates of and .

- A ,
- B ,
- C ,
- D ,
- E ,

Using the fact that a reflection in a line through the origin is a linear transformation, find the matrix which represents reflection in the line .

- A
- B
- C
- D
- E

**Q3: **

A linear transformation of a plane sends the vector to . If the transformation is a rotation, where does it send ?

- A
- B
- C
- D
- E

**Q4: **

Let be a linear transformation. Suppose the matrix for relative to a basis for is . Suppose is the transition matrix from another basis to . Determine the matrix for with respect to .

- A
- B
- C
- D

**Q5: **

Shape A has been translated to Shape B and then to Shape C.

Write a vector to represent the translation from Shape A to Shape B.

- A
- B
- C
- D
- E

Write a vector to represent the translation from Shape B to Shape C.

- A
- B
- C
- D
- E

Write a vector to represent the translation from Shape C to Shape A.

- A
- B
- C
- D
- E