1. 1
   Point A has coordinates (2, 5). It is translated by the column vector $\begin{pmatrix} 4 \\ -3 \end{pmatrix}$ to give point A'. A' is then translated by the column vector $\begin{pmatrix} -1 \\ 2 \end{pmatrix}$ to give point A''.

   (a)

   What are the coordinates of A'?

   [1 mark]

   • A(6, 2)
   • B(-2, 8)
   • C(6, -8)
   • D(2, -3)

   (b)

   What are the coordinates of A''?

   [1 mark]

   • A(6, 2)
   • B(5, 4)
   • C(3, 9)
   • D(5, -1)

   (c)

   What single column vector maps A directly to A''?

   [1 mark]

   • A$\begin{pmatrix} -3 \\ 1 \end{pmatrix}$
   • B$\begin{pmatrix} 5 \\ -1 \end{pmatrix}$
   • C$\begin{pmatrix} 3 \\ 1 \end{pmatrix}$
   • D$\begin{pmatrix} 3 \\ -1 \end{pmatrix}$

   Total for question 1: 3 marks

2. 2
   Point B has coordinates (3, -2). It is reflected in the line y = x to give point B'. B' is then reflected in the x-axis to give point B''.

   (a)

   Find the coordinates of B'.

   [2 marks]

   (b)

   Find the coordinates of B''.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Triangle has a vertex P at (1, 2). It is rotated 90° clockwise about the origin O to give vertex P'. The image is then enlarged by scale factor 3, centre the origin, to give vertex P''.

   (a)

   Find the coordinates of P'.

   [3 marks]

   (b)

   Find the coordinates of P''.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Shape S1 has a vertex X at (2, 1). S1 is translated by the column vector $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ to form shape S2, then S2 is rotated 180° about the point (7, 1) to form shape S3.

   (a)

   Find the coordinates of the image of vertex X, (2, 1), of shape S1 after it is translated by the column vector $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ to form shape S2.

   [4 marks]

   (b)

   Using your answer to part (a), find the coordinates of the corresponding vertex of shape S3.

   [4 marks]

   (c)

   Describe fully the single transformation that maps shape S1 directly to shape S3.

   [5 marks]

   Total for question 4: 13 marks

End of questions