AQA
Further Paper 2
2024
June
Q12
5 marks
Challenging +1.2
12
The transformation S is represented by the matrix \(\mathbf { M } = \left[ \begin{array} { c c } 1 & - 6 \\ 2 & 7 \end{array} \right]\)
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.