A geometric transformation $T:\binom{x}{y} \mapsto\binom{x^{\prime}}{y^{\prime}}$ is defined by $$ T:\binom{x^{\prime}}{y^{\prime}}=\left(\begin{array}{cc} 7 -10 2 -3 \end{array}\right)\binom{x}{y}+\binom{-5}{4} $$

$\left(\begin{array}{cc}7 & -10 \\ 2 & -3\end{array}\right)\binom{6}{-2}+\binom{-5}{4}$ (M1) $=\binom{57}{22}$ OR $(57,22)$ A1 [2 marks]

$\binom{2p}{2q}=\left(\begin{array}{cc}7 & -10 \\ 2 & -3\end{array}\right)\binom{p}{q}+\binom{-5}{4}$ $7p-10q-5=2p$ $2p-3q+4=2q$ solve simultaneously: $p=13, q=6$ A1 Note: Award $\boldsymbol{A0}$ if 13 and 6 are not labelled or are labelled the other way around.

$\operatorname{det}\left(\begin{array}{cc}7 & -10 \\ 2 & -3\end{array}\right)=-1\left(\mathrm{OR}\left|\operatorname{det}\left(\begin{array}{ll}7 & -10 \\ 2 & -3\end{array}\right)\right|=1\right)$ scale factor of image area is therefore $(|-1|=) 1$ (and the translation does not affect the area)