7. The matrix $\mathbf { A }$ is defined by

$$\mathbf { A } = \left( \begin{array} { r r } 
4 & - 5 \\
- 3 & 2
\end{array} \right)$$

The transformation represented by $\mathbf { A }$ maps triangle $T$ onto triangle $T ^ { \prime }$

Given that the area of triangle $T$ is $23 \mathrm {~cm} ^ { 2 }$
\begin{enumerate}[label=(\alph*)]
\item determine the area of triangle $T ^ { \prime }$\\
(2)

The point $P$ has coordinates ( $3 p + 2,2 p - 1$ ) where $p$ is a constant. The transformation represented by $\mathbf { A }$ maps $P$ onto the point $P ^ { \prime }$ with coordinates $( 17 , - 18 )$
\item Determine the value of $p$.

Given that

$$\mathbf { B } = \left( \begin{array} { r r } 
0 & 1 \\
- 1 & 0
\end{array} \right)$$
\item describe fully the single geometrical transformation represented by matrix $\mathbf { B }$

The transformation represented by matrix $\mathbf { A }$ followed by the transformation represented by matrix $\mathbf { C }$ is equivalent to the transformation represented by matrix $\mathbf { B }$
\item Determine C\\

\includegraphics[max width=\textwidth, alt={}, center]{f8660b02-384e-460f-a0e4-282ef5fef475-21_2255_50_314_34}\\

\begin{center}

\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2021 Q7 [9]}}