June 2019 Paper 1 Q14
14 Here are two transformations.
A \(\qquad\) Rotation \(90^\circ\) clockwise about the origin.
B \(\qquad\) Reflection in the line \(\quad y = x\)
Use matrix multiplication to work out the single matrix which represents the combined transformation A followed by B. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((\mathrm{A} =)\ \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) | B1 | |
| \((\mathrm{B} =)\ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) | B1 | |
| \((\mathrm{BA} =)\ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\) | M1 | must be two 2x2 matrices in the correct order |
| \(\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) | A1 | only if M1 awarded for correct product |
Additional guidance
| Mark positively for the B marks (you may see more than 2 matrices) | |
| If both matrices wrong but then in the correct order | B0, B0, M1, A0 |
| Both matrices correct but in wrong order | B1, B1, M0, A0 |
| Possible to score B1 B0 M1 A0 if one correct and one not | B1, B0, M1, A0 |
| Either A or B on answer line but not identified and no other working | B0, B0, M0, A0 |
| Condone matrices written without brackets throughout |