Matrix representations of standard transformations Quiz

1. Which matrix represents reflection in the $x$-axis?

• A. $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$
• B. $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$
• C. $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
• D. $\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}$

2. The matrix $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ represents which transformation?

• A. Rotation $90^\circ$ clockwise about $O$
• B. Reflection in $y=x$
• C. Rotation $90^\circ$ anticlockwise about $O$
• D. Reflection in $y=-x$

3. What is the image of $(2,5)$ under the enlargement with centre $O$ and scale factor $-3$?

• A. $(-6,-15)$
• B. $(6,15)$
• C. $(-2,-5)$
• D. $(6,-15)$

4. A stretch parallel to the $y$-axis with scale factor $4$ acts on $(3,2)$. What is the image?

• A. $(12,2)$
• B. $(3,8)$
• C. $(12,8)$
• D. $(7,2)$

5. A rotation through $\theta$ anticlockwise has matrix $\begin{pmatrix} \frac12 & -\frac{\sqrt3}{2} \\ \frac{\sqrt3}{2} & \frac12 \end{pmatrix}$. Find $\theta$.

• A. $30^\circ$
• B. $120^\circ$
• C. $45^\circ$
• D. $60^\circ$