AQA
Further Paper 2
2024
June
Q12
5 marks
Challenging +1.2
The transformation \(S\) is represented by the matrix \(\mathbf{M} = \begin{bmatrix} 1 & -6 \\ 2 & 7 \end{bmatrix}\)
The transformation \(T\) is a reflection in the line \(y = x\sqrt{3}\) and is represented by the matrix \(\mathbf{N}\)
The point \(P(x, y)\) is transformed first by \(S\), then by \(T\)
The result of these transformations is the point \(Q(3, 8)\)
Find the coordinates of \(P\)
Give your answers to three decimal places.
[5 marks]