Problem

6. $A = \begin{pmatrix} 2 & 3 \\ 1 & -4 \end{pmatrix}$

The transformation represented by $A$ maps the point $R(3p - 13, p - 4)$, where $p$ is a constant, onto the point $R'(7, -2)$

(a) Determine the value of $p$

The point $S$ has coordinates $(0, 7)$

Given that $O$ is the origin,

(b) determine the area of triangle $ORS$

The transformation represented by $A$ maps the triangle $ORS$ onto the triangle $OR'S'$

(c) Hence, using your answer to part (b), determine the area of triangle $OR'S'$