IAL 2019 May FP1 Q2

Question

[!problem]

The matrix $M$ is given by

$M = \begin{pmatrix} 4 & k - 12 \\ 3 & k \end{pmatrix}$

where $k$ is a real constant.

The transformation represented by the matrix $M$ transforms hexagon $R$ to hexagon $S$.

The area of hexagon $R$ is 20 square units and the area of hexagon $S$ is 320 square units.

Find the possible values of $k$.

(5)