1Work out $\begin{pmatrix}4 & -2 \\ 4 & 2\end{pmatrix}\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$, where $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$ is the identity matrix.
A$\begin{pmatrix}4 & -1 \\ 4 & 2\end{pmatrix}$B$\begin{pmatrix}2 & 4 \\ -2 & 4\end{pmatrix}$C$\begin{pmatrix}4 & -2 \\ 4 & 2\end{pmatrix}$D$\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$
2Describe fully the single transformation represented by the matrix $\begin{pmatrix}4 & 0 \\ 0 & 4\end{pmatrix}$.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Enlargement, scale factor }5\text{, centre the origin}$C$\text{Enlargement, scale factor }4\text{, centre the origin}$D$\text{Stretch, scale factor }4\text{, parallel to the }x\text{-axis}$
3The transformation with matrix $\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$ maps points onto their images.
Find the image of the point $(4,\ 0)$.
A$(0,\ -4)$B$(-4,\ 0)$C$(4,\ 0)$D$(0,\ 4)$
4The point $(-2,\ -1)$ is mapped by a reflection in the line $y=x$.
Find the coordinates of its image.
A$(1,\ 2)$B$(-2,\ -1)$C$(2,\ -1)$D$(-1,\ -2)$
5Write down the $2 \times 2$ matrix that represents a rotation of 90° clockwise about the origin.
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$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
6A transformation maps $(1,0)$ to $(1,\ 0)$ and $(0,1)$ to $(0,\ -1)$.
Write down the $2 \times 2$ matrix of this transformation.
A$\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$B$\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$C$\begin{pmatrix}1 & 1 \\ 0 & -1\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$
7Work out $\begin{pmatrix}3 & 1 \\ 2 & 1\end{pmatrix}\begin{pmatrix}2 & 3 \\ 0 & 3\end{pmatrix}$.
A$\begin{pmatrix}12 & 5 \\ 6 & 3\end{pmatrix}$B$\begin{pmatrix}6 & 3 \\ 0 & 3\end{pmatrix}$C$\begin{pmatrix}7 & 12 \\ 4 & 9\end{pmatrix}$D$\begin{pmatrix}6 & 12 \\ 4 & 9\end{pmatrix}$
8A shape has area $5\text{ cm}^2$.
It is enlarged by the matrix $\begin{pmatrix}3 & 0 \\ 0 & 3\end{pmatrix}$.
Work out the area of the image.
A15B30C14D45
9The unit square has vertices $O(0,0)$, $A(1,0)$, $B(1,1)$ and $C(0,1)$.
The transformation with matrix $\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$ maps the square onto its image.
Find the coordinates of the image of $C$.
A$(0,\ -1)$B$(1,\ 0)$C$(0,\ 1)$D$(-1,\ 0)$
10Describe fully the single transformation represented by the matrix $\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}$.
A$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$B$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$C$\text{Reflection in the line }y=-x$D$\text{Rotation }180^{\circ}\text{ about the origin}$
11A transformation maps $(1,0)$ to $(0,\ -1)$ and $(0,1)$ to $(-1,\ 0)$.
Write down the $2 \times 2$ matrix of this transformation.
A$\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}$B$\begin{pmatrix}0 & 0 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
12A point is transformed by a rotation of 180° about the origin, followed by a reflection in the $x$-axis.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Reflection in the }y\text{-axis}$C$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$D$\text{Reflection in the line }y=x$
13A shape is transformed by a rotation of 90° anticlockwise about the origin, followed by a reflection in the $x$-axis.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$D$\begin{pmatrix}0 & -1 \\ 0 & 0\end{pmatrix}$
14A point is transformed by a rotation of 90° anticlockwise about the origin, followed by a rotation of 90° anticlockwise about the origin.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$B$\text{Reflection in the line }y=-x$C$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$D$\text{Rotation }180^{\circ}\text{ about the origin}$
15A shape is transformed by a rotation of 90° clockwise about the origin, followed by a reflection in the $y$-axis.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$D$\begin{pmatrix}0 & -1 \\ 0 & 0\end{pmatrix}$