Transformation Topic Question [Pearson Edexcel Mathematics B (4MB1) 2014-2016]

 

1	(Edexcel/Math B/2014/jan/paper02/q11) The points (1, 0), (2, 3) and (3, 2) are the vertices of triangle A. (a) On the grid, draw and label triangle A. (1) Triangle A is transformed to triangle B by an enlargement with scale factor 2 and centre (0, 0). (b) (i) Write down the coordinates of the vertices of triangle B. (ii) On the grid, draw and label triangle B. ............(2) \( \mathbf{S}=\left(\begin{array}{rr}0 & -\frac{1}{2} \\ 1 & 0\end{array}\right) \)        Triangle B is transformed to triangle C under the transformation with matrix S. (c) (i) Find the coordinates of triangle C. (ii) On the grid, draw and label triangle C. (3)  \( \mathbf{T}=\left(\begin{array}{rr}0 & \frac{1}{2} \\ 1 & 0\end{array}\right) \)        Triangle C is transformed to triangle D under the transformation with matrix T. (d) (i) Find the coordinates of triangle D. (ii) On the grid, draw and label triangle D. (3) (e) Describe fully the single transformation which transforms triangle A to triangle D. (1) (Total for Question 11 is 10 marks)
2	(Edexcel/Math B/2014/janR/paper02/q8) The points A (–3, 4), B (–1, 5) and C (–1, 4) are the vertices of a triangle ABC. (a) On the grid, draw and label triangle ABC. (1) \( \mathbf{R}=\left(\begin{array}{rr}0 & -1 \\ -1 & 0\end{array}\right) \) (b) Calculate the matrix product R \( \mathbf{R}=\left(\begin{array}{rr}-3 & -1 & -1 \\ 4 & 5 & 4\end{array}\right) \) (2) Triangle A'B'C' is the image of triangle ABC, where A', B' and C' are respectively the images of A, B and C, under the transformation with matrix R. (c) On the grid, draw and label triangle A'B'C' (2) (d) Describe fully the single transformation which maps triangle ABC onto triangle A'B'C' (2) Triangle A"B"C" is the image of triangle A'BC, where A", B" and C" are respectively the images of A', B' and C', under the enlargement centre (–1.5, 1.5) with scale factor –1 (e) On the grid, draw and label triangle A"B"C" (2) (f) Describe fully the single transformation which maps triangle A"B"C" onto triangle ABC. (2)
3	(Edexcel/Math B/2014/june/paper02/q7) The points (2, 3), (4, 3) and (4, 4) are the vertices of a triangle A. (a) On the grid, draw and label triangle A. (1) Triangle A is transformed to triangle B under the translation \( \left(\begin{array}{rr} 0 \\ -5 \end{array}\right) \) . (b) On the grid, draw and label triangle B. (1) Triangle B is transformed to triangle C under the transformation with matrix T where \( \mathbf{T}=\left(\begin{array}{rr}-2 & 0 \\ 0 & -2\end{array}\right) \) (c) Find the coordinates of the vertices of triangle C. (2) (d) On the grid, draw and label triangle C. (1) Triangle B is mapped to triangle C under the transformation with matrix T by an anticlockwise rotation about the origin of 180° followed by an enlargement with centre the origin. (e) Find the scale factor of this enlargement. (1) Triangle C is transformed to triangle D under the translation \( \left(\begin{array}{rr}0 \\ 5\end{array}\right) \)  (f) On the grid, draw and label triangle D. (1) Triangle A is transformed to triangle D by a single enlargement. (g) Describe fully this enlargement. (2) (Total for Question 7 is 9 marks)
4	(Edexcel/Math B/2014/juneR/paper02/q9) The points (–5, –4), (–5, –6) and (–2, –4) are the vertices of triangle P. (a) On the grid opposite, draw and label triangle P. (1) Triangle Q is the image of triangle P under a reflection in the line with equation y = –1 (b) On the grid, draw and label the line of reflection. (1) (c) On the grid, draw and label triangle Q. (1) Triangle Q is transformed to triangle R under the transformation with matrix M where \( \mathbf{M}=\left(\begin{array}{rr}-1 & -1 \\ 1 & 3\end{array}\right) \) (d) On the grid, draw and label triangle R. (3) (e) On the grid, translate triangle R by the vector \( \left(\begin{array}{rr}4 \\ -12\end{array}\right) \) . Label this triangle S. (2) Triangle S is transformed to triangle T under the transformation with matrix N where \( \mathbf{N}=\left(\begin{array}{rr}-\frac{3}{2} & -\frac{1}{2} \\\frac{1}{2} & \frac{1}{2}\end{array}\right) \) (f) On the grid, draw and label triangle T. (3) (g) Describe fully the single transformation which maps triangle T onto triangle P. (2) (Total for Question 9 is 13 marks)
	to be continued....

Answer Key

1.   (a) Triangle A drawn and labelled (b)(i) $\left(\begin{array}{ccc}2 & 4 & 6 \\0 & 6 & 4\end{array}\right) \quad$ (ii) Triangle B drawn and labelled (c) (i) $\left(\begin{array}{ccc}0 & -3 & -2 \\2 & 4 & 6\end{array}\right)$ (ii) Triangle  C  drawn and labelled (d)(i) $\left(\begin{array}{ccc}1 & 2 & 3 \\0 & -3 & -2\end{array}\right)$ (ii) Triangle D drawn and labelled (e) Reflection in $x-axis$
2.   (a) triangle $A B C$ (b) $\left(\begin{array}{ccc}-4 & -5 & -4 \\ 3 & 1 & 1\end{array}\right)$ (c) triangle $A^{\prime} B^{\prime} C^{\prime}$ (d). reflection; $y=-x$ (e)one vertex correctly identified. triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ correct (f) reflection, $y=x+3$
3.   (a) Triangle $A$ draw and labelled (b) Triangle $B\left(\begin{array}{ccc}2 & 4 & 4 \\ -2 & -2 & -1\end{array}\right)$ (c) $C(-4,4),(-8,4),(-8,2)$ (d) Triangle $C$ drawn and labelled (e) scale factor $=2 \quad$ (f) Triangle $D=\left(\begin{array}{ccc}-4 & -8 & -8 \\ 9 & 9 & 7\end{array}\right)$ (g) enlargement centre $(0,5)$ with scale facter -2
4.   (a) Triarigle $P$ drawn and labelled (b) $y=-1$ drawn and labelled (c) Triangle $Q$ drawn and labelled $(-5,2)(-5,4)(-2,2)$ (d) Triangle $R$ drawn and labelled $(3,1)(1,7)(0,4)$ (e) Triangle $S$ drawn and labelled $(7,-11)(5,-5)(4,-8)$ (f) Triangle $T$ drawn and labelled $(-5,-2)(-5,0)(-2,-2)$ (g) Reflection $y=-3$
5.   (a) $A$ drawn $\&$ labelled (b) $B(-1,0),(-3,0)(1,-2)$ (c) $B$ drawn and labelled (d) $(-1,-2)(-3,-6)(-1,-6)$ (e) $C$ drawn and labelled (f) Reflection in $y=-x$
6.   (a) Triangle $A$, (b) $y=-1$, (c) Triangle $B$ (d) Triangle $C$ (e) Triangle $D$ (f) Reflection $x=0$ or $y$ axis (g) Enlargement, Scale factor 2 , centre $(0,-4)$
7.   (a) A draw and labeled (b) B draw and labelled (c) C draw and labelled (d) D draw and labeled. (e) Reflection in $x$-axis
8.   $(-3,5)$ 
9.   (a) $(-1,-1) \quad$ (b) $\left(\begin{array}{ccc}-3 & -5 & -6 \\ 1 & 4 &  \end{array}\right)$ (c) $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ (d) Reflection , $x=-1$
10.   $\theta=180, a=1$ or $x=1$
11.   (a) $\triangle ABC drawn$ (b) $\left(\begin{array}{ccc}4 & 6 & 8 \\ 0 & 0 & 3\end{array}\right)$ (c) $\triangle A^{\prime} B^{\prime} C^{\prime}$ draw (d) $\triangle A^{\prime} B^{\prime} C^{\prime}=\left(\begin{array}{ccc}-4 & -6 & -8 \\ -4 & -6 & -2\end{array}\right)$ draw (e) enlargement, centre origin, scale Factor -2 (f) $\left(\begin{array}{cc}-2 & 0 \\ 0 & -2\end{array}\right)$
12.   (a) Rotation, $90^{\circ}$ clockwise, About $(-3,1)$ (b) diagram
13.   (a) $90^\circ$ (b) $\left(\begin{array}{cc}-{0} & {-1} \\ 1 & 0   \end{array}\right)$ (c) $\left(\begin{array}{c}{-1} \\ {-6}  \end{array}\right)$
14.   (a) Diagram (b) Diagram (c) Diagram (d) Rotation, about origin or $(0,0)$ (anticlockwise) $270^{\circ}$ or clock wise $90^{\circ}$ or $-90^{\circ}$