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Matrix Transformations · MCQ assessment

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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

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1Work out $\begin{pmatrix}1 & 1 \\ -1 & 3\end{pmatrix}\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$, where $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$ is the identity matrix.
A$\begin{pmatrix}3 & -1 \\ 1 & 1\end{pmatrix}$B$\begin{pmatrix}1 & 1 \\ -1 & 3\end{pmatrix}$C$\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$D$\begin{pmatrix}1 & 2 \\ -1 & 3\end{pmatrix}$
2Work out $\begin{pmatrix}2 & 0 \\ 0 & 2\end{pmatrix}\begin{pmatrix}3 \\ 5\end{pmatrix}$.
Give your answer as a column vector.
A$\begin{pmatrix}10 \\ 6\end{pmatrix}$B$\begin{pmatrix}9 \\ 5\end{pmatrix}$C$\begin{pmatrix}6 \\ 10\end{pmatrix}$D$\begin{pmatrix}-6 \\ -10\end{pmatrix}$
3Write down the $2 \times 2$ matrix that represents a reflection in the line $y=x$.
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$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
4The transformation with matrix $\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$ maps points onto their images.
Find the image of the point $(-3,\ 1)$.
A$(-1,\ 3)$B$(-3,\ 1)$C$(-3,\ -1)$D$(1,\ -3)$
5Describe fully the single transformation represented by the matrix $\begin{pmatrix}5 & 0 \\ 0 & 5\end{pmatrix}$.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Stretch, scale factor }5\text{, parallel to the }x\text{-axis}$C$\text{Enlargement, scale factor }6\text{, centre the origin}$D$\text{Enlargement, scale factor }5\text{, centre the origin}$
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$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}1 & 1 \\ 0 & -1\end{pmatrix}$D$\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$
7The 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$(0,\ -2)$D$(1,\ 0)$
8Describe fully the single transformation represented by the matrix $\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Reflection in the line }y=x$C$\text{Reflection in the }y\text{-axis}$D$\text{Reflection in the }x\text{-axis}$
9Work out $\begin{pmatrix}2 & 0 \\ 1 & 3\end{pmatrix}\begin{pmatrix}3 & 3 \\ 0 & 1\end{pmatrix}$.
A$\begin{pmatrix}7 & 6 \\ 3 & 6\end{pmatrix}$B$\begin{pmatrix}6 & 6 \\ 3 & 6\end{pmatrix}$C$\begin{pmatrix}6 & 0 \\ 0 & 3\end{pmatrix}$D$\begin{pmatrix}9 & 9 \\ 1 & 3\end{pmatrix}$
10A shape has area $3\text{ cm}^2$.
It is enlarged by the matrix $\begin{pmatrix}4 & 0 \\ 0 & 4\end{pmatrix}$.
Work out the area of the image.
A12B19C24D48
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$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$D$\begin{pmatrix}0 & 2 \\ -1 & 0\end{pmatrix}$
12A point is transformed by a reflection in the $x$-axis, followed by a reflection in the line $y=x$.
Describe fully the single transformation that has the same effect.
A$\text{Reflection in the }y\text{-axis}$B$\text{Reflection in the }x\text{-axis}$C$\text{Rotation }180^{\circ}\text{ about the origin}$D$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$
13A shape is transformed by a rotation of 90° anticlockwise about the origin, followed by a reflection in the line $y=-x$.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
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$\begin{pmatrix}-1 & 0 \\ 1 & 1\end{pmatrix}$
14A point is transformed by a reflection in the $y$-axis, followed by a reflection in the line $y=x$.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Reflection in the }x\text{-axis}$C$\text{Reflection in the line }y=-x$D$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$
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$\begin{pmatrix}0 & -1 \\ 0 & 0\end{pmatrix}$
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Matrix Transformations · MCQ assessment

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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

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123456789101112131415
/ 15
1Work out $\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}5 \\ 4\end{pmatrix}$.
Give your answer as a column vector.
A$\begin{pmatrix}5 \\ -4\end{pmatrix}$B$\begin{pmatrix}-5 \\ 4\end{pmatrix}$C$\begin{pmatrix}-4 \\ 5\end{pmatrix}$D$\begin{pmatrix}10 \\ -8\end{pmatrix}$
2Work out $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}\begin{pmatrix}2 & 4 \\ 4 & 3\end{pmatrix}$, where $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$ is the identity matrix.
A$\begin{pmatrix}3 & 4 \\ 4 & 2\end{pmatrix}$B$\begin{pmatrix}2 & 5 \\ 4 & 3\end{pmatrix}$C$\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$D$\begin{pmatrix}2 & 4 \\ 4 & 3\end{pmatrix}$
3Describe fully the single transformation represented by the matrix $\begin{pmatrix}5 & 0 \\ 0 & 5\end{pmatrix}$.
A$\text{Stretch, scale factor }5\text{, parallel to the }x\text{-axis}$B$\text{Rotation }180^{\circ}\text{ about the origin}$C$\text{Enlargement, scale factor }5\text{, centre the origin}$D$\text{Enlargement, scale factor }6\text{, centre the origin}$
4The transformation with matrix $\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$ maps points onto their images.
Find the image of the point $(-4,\ 4)$.
A$(-4,\ -5)$B$(-3,\ -2)$C$(-4,\ -4)$D$(4,\ 4)$
5Write down the $2 \times 2$ matrix that represents a rotation of 90° clockwise about the origin.
A$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$D$\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$
6Describe fully the single transformation represented by the matrix $\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Reflection in the }x\text{-axis}$C$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$D$\text{Reflection in the line }y=-x$
7A shape has area $6\text{ cm}^2$.
It is enlarged by the matrix $\begin{pmatrix}5 & 0 \\ 0 & 5\end{pmatrix}$.
Work out the area of the image.
A30B31C60D150
8Work out $\begin{pmatrix}1 & 1 \\ 1 & 2\end{pmatrix}\begin{pmatrix}3 & 2 \\ 2 & 2\end{pmatrix}$.
A$\begin{pmatrix}5 & 7 \\ 4 & 6\end{pmatrix}$B$\begin{pmatrix}6 & 4 \\ 7 & 6\end{pmatrix}$C$\begin{pmatrix}5 & 4 \\ 7 & 6\end{pmatrix}$D$\begin{pmatrix}3 & 2 \\ 2 & 4\end{pmatrix}$
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 $A$.
A$(1,\ 0)$B$(0,\ 1)$C$(0,\ -1)$D$(0,\ 3)$
10A 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$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$C$\begin{pmatrix}-1 & 1 \\ 0 & 1\end{pmatrix}$D$\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$
11Describe fully the single transformation represented by the matrix $\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$.
A$\text{Reflection in the }y\text{-axis}$B$\text{Reflection in the }x\text{-axis}$C$\text{Rotation }180^{\circ}\text{ about the origin}$D$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$
12A point is transformed by a reflection in the $x$-axis, followed by a reflection in the line $y=x$.
Describe fully the single transformation that has the same effect.
A$\text{Reflection in the }x\text{-axis}$B$\text{Rotation }180^{\circ}\text{ about the origin}$C$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$D$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$
13A 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$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$B$\begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & -1 \\ 0 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
14A point is transformed by a reflection in the line $y=x$, followed by a reflection in the $x$-axis.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$B$\text{Reflection in the }y\text{-axis}$C$\text{Reflection in the line }y=-x$D$\text{Rotation }180^{\circ}\text{ about the origin}$
15A shape is transformed by a reflection in the $y$-axis, followed by a reflection in the line $y=-x$.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & -1 \\ 2 & 0\end{pmatrix}$B$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$
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Matrix Transformations · MCQ assessment

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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

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/ 15
1Work out $\begin{pmatrix}2 & 0 \\ 0 & 2\end{pmatrix}\begin{pmatrix}3 \\ 4\end{pmatrix}$.
Give your answer as a column vector.
A$\begin{pmatrix}9 \\ 4\end{pmatrix}$B$\begin{pmatrix}6 \\ 8\end{pmatrix}$C$\begin{pmatrix}-6 \\ -8\end{pmatrix}$D$\begin{pmatrix}8 \\ 6\end{pmatrix}$
2Work out $\begin{pmatrix}3 & -3 \\ -2 & 3\end{pmatrix}\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$, where $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$ is the identity matrix.
A$\begin{pmatrix}3 & -2 \\ -3 & 3\end{pmatrix}$B$\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$C$\begin{pmatrix}3 & -2 \\ -2 & 3\end{pmatrix}$D$\begin{pmatrix}3 & -3 \\ -2 & 3\end{pmatrix}$
3The transformation with matrix $\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$ maps points onto their images.
Find the image of the point $(-1,\ -4)$.
A$(1,\ -4)$B$(-1,\ 4)$C$(1,\ -5)$D$(-4,\ 1)$
4Write 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$\begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
5The point $(3,\ 1)$ is mapped by a reflection in the line $y=-x$.
Find the coordinates of its image.
A$(-3,\ -1)$B$(-3,\ 1)$C$(1,\ 3)$D$(-1,\ -3)$
6The unit square has vertices $O(0,0)$, $A(1,0)$, $B(1,1)$ and $C(0,1)$.
The transformation with matrix $\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}$ maps the square onto its image.
Find the coordinates of the image of $B$.
A$(-3,\ -2)$B$(1,\ 1)$C$(-1,\ -1)$D$(-1,\ 1)$
7A transformation maps $(1,0)$ to $(3,\ 0)$ and $(0,1)$ to $(0,\ 3)$.
Write down the $2 \times 2$ matrix of this transformation.
A$\begin{pmatrix}-3 & 0 \\ 0 & -3\end{pmatrix}$B$\begin{pmatrix}3 & 0 \\ 0 & 3\end{pmatrix}$C$\begin{pmatrix}3 & 1 \\ 0 & 3\end{pmatrix}$D$\begin{pmatrix}0 & 3 \\ 3 & 0\end{pmatrix}$
8Work out $\begin{pmatrix}2 & 1 \\ 3 & 2\end{pmatrix}\begin{pmatrix}3 & 0 \\ 1 & 3\end{pmatrix}$.
A$\begin{pmatrix}6 & 3 \\ 11 & 7\end{pmatrix}$B$\begin{pmatrix}8 & 3 \\ 11 & 6\end{pmatrix}$C$\begin{pmatrix}7 & 3 \\ 11 & 6\end{pmatrix}$D$\begin{pmatrix}6 & 0 \\ 3 & 6\end{pmatrix}$
9Describe fully the single transformation represented by the matrix $\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$.
A$\text{Reflection in the }y\text{-axis}$B$\text{Reflection in the line }y=x$C$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$D$\text{Rotation }180^{\circ}\text{ about the origin}$
10A shape has area $12\text{ cm}^2$.
It is enlarged by the matrix $\begin{pmatrix}4 & 0 \\ 0 & 4\end{pmatrix}$.
Work out the area of the image.
A48B28C96D192
11The 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$(1,\ 0)$
12A point is transformed by a reflection in the $y$-axis, followed by a reflection in the line $y=x$.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$B$\text{Reflection in the }y\text{-axis}$C$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$D$\text{Reflection in the }x\text{-axis}$
13A shape is transformed by a reflection in the $y$-axis, followed by a reflection in the line $y=-x$.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & -1 \\ 2 & 0\end{pmatrix}$B$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$
14A shape is transformed by a reflection in the line $y=-x$, followed by a reflection in the $x$-axis.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & -1 \\ 2 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$D$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$
15A point is transformed by a reflection in the line $y=-x$, followed by a reflection in the $x$-axis.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$B$\text{Reflection in the }y\text{-axis}$C$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$D$\text{Reflection in the line }y=x$
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Matrix Transformations · MCQ assessment

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Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

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123456789101112131415
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1Work out $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}\begin{pmatrix}3 & -3 \\ 0 & 3\end{pmatrix}$, where $\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$ is the identity matrix.
A$\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}$B$\begin{pmatrix}3 & 0 \\ -3 & 3\end{pmatrix}$C$\begin{pmatrix}3 & -2 \\ 0 & 3\end{pmatrix}$D$\begin{pmatrix}3 & -3 \\ 0 & 3\end{pmatrix}$
2Work out $\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}\begin{pmatrix}1 \\ 2\end{pmatrix}$.
Give your answer as a column vector.
A$\begin{pmatrix}1 \\ 2\end{pmatrix}$B$\begin{pmatrix}-1 \\ -2\end{pmatrix}$C$\begin{pmatrix}0 \\ -4\end{pmatrix}$D$\begin{pmatrix}-2 \\ -1\end{pmatrix}$
3The transformation with matrix $\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$ maps points onto their images.
Find the image of the point $(-2,\ -1)$.
A$(2,\ -1)$B$(-1,\ 1)$C$(-2,\ 1)$D$(1,\ -2)$
4The point $(3,\ 0)$ is mapped by a reflection in the $y$-axis.
Find the coordinates of its image.
A$(0,\ -3)$B$(-3,\ 1)$C$(3,\ 0)$D$(-3,\ 0)$
5Write down the $2 \times 2$ matrix that represents a 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$\begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$
6A transformation maps $(1,0)$ to $(0,\ 1)$ and $(0,1)$ to $(-1,\ 0)$.
Write down the $2 \times 2$ matrix of this transformation.
A$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & 0 \\ 1 & 0\end{pmatrix}$C$\begin{pmatrix}-1 & 0 \\ 0 & 1\end{pmatrix}$D$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$
7A shape has area $3\text{ cm}^2$.
It is enlarged by the matrix $\begin{pmatrix}3 & 0 \\ 0 & 3\end{pmatrix}$.
Work out the area of the image.
A18B9C27D12
8Describe fully the single transformation represented by the matrix $\begin{pmatrix}-1 & 0 \\ 0 & -1\end{pmatrix}$.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$C$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$D$\text{Reflection in the }x\text{-axis}$
9Work out $\begin{pmatrix}2 & 3 \\ 0 & 3\end{pmatrix}\begin{pmatrix}3 & 3 \\ 0 & 3\end{pmatrix}$.
A$\begin{pmatrix}6 & 9 \\ 0 & 9\end{pmatrix}$B$\begin{pmatrix}6 & 15 \\ 0 & 9\end{pmatrix}$C$\begin{pmatrix}6 & 18 \\ 0 & 9\end{pmatrix}$D$\begin{pmatrix}7 & 15 \\ 0 & 9\end{pmatrix}$
10The 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$(0,\ 1)$C$(-1,\ 0)$D$(1,\ 0)$
11A transformation maps $(1,0)$ to $(3,\ 0)$ and $(0,1)$ to $(0,\ 3)$.
Write down the $2 \times 2$ matrix of this transformation.
A$\begin{pmatrix}3 & 0 \\ 0 & 3\end{pmatrix}$B$\begin{pmatrix}0 & 3 \\ 3 & 0\end{pmatrix}$C$\begin{pmatrix}3 & 1 \\ 0 & 3\end{pmatrix}$D$\begin{pmatrix}-3 & 0 \\ 0 & -3\end{pmatrix}$
12A point is transformed by a reflection in the $x$-axis, followed by a reflection in the line $y=x$.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }180^{\circ}\text{ about the origin}$B$\text{Reflection in the line }y=-x$C$\text{Reflection in the line }y=x$D$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$
13A shape is transformed by a reflection in the line $y=-x$, 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$\begin{pmatrix}0 & 1 \\ 0 & 0\end{pmatrix}$
14A point is transformed by a rotation of 180° about the origin, followed by a reflection in the $y$-axis.
Describe fully the single transformation that has the same effect.
A$\text{Rotation }90^{\circ}\text{ anticlockwise about the origin}$B$\text{Reflection in the }x\text{-axis}$C$\text{Reflection in the line }y=-x$D$\text{Rotation }90^{\circ}\text{ clockwise about the origin}$
15A shape is transformed by a reflection in the $y$-axis, followed by a reflection in the line $y=x$.
Work out the single $2 \times 2$ matrix that represents the combined transformation.
A$\begin{pmatrix}0 & 1 \\ -1 & 0\end{pmatrix}$B$\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$C$\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}$D$\begin{pmatrix}0 & 1 \\ 0 & 0\end{pmatrix}$
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