AS June 2023 Paper 1 Q1
1 The transformation R of the plane is reflection in the line \(x = 0\).
(a) Write down the matrix \(\mathbf{M}\) associated with R. [1]
(b) Find \(\mathbf{M}^2\). [1]
(c) Interpret the result of part (b) in terms of the transformation R. [1]
| Scheme | Marks | AO |
|---|---|---|
| \(\mathbf{M} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) | B1 | 1.1 |
| [1] |
Notes
B1: must be 2 by 2
| Scheme | Marks | AO |
|---|---|---|
| \(\mathbf{M}^2 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) | B1 | 1.1 |
| [1] |
Notes
B1: Condone from \(\mathbf{M} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\)
| Scheme | Marks | AO |
|---|---|---|
| [\(\mathbf{M}^2\) is the identity matrix] It represents the combination of two reflections, which is the identity transformation. | B1 | 2.4 |
| [1] |
Notes
B1: \(\mathbf{M}^2\) must be an identity matrix (condone \(3 \times 3\))
oe, e.g. R is self-inverse