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 \(23 \mathrm {~cm} ^ { 2 }\)
- 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 \(( 17 , - 18 )\)
- Determine the value of \(p\).
Given that
$$\mathbf { B } = \left( \begin{array} { r r }
0 & 1 \\
- 1 & 0
\end{array} \right)$$
- 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 \(\mathbf { B }\)
- Determine C
\includegraphics[max width=\textwidth, alt={}, center]{f8660b02-384e-460f-a0e4-282ef5fef475-21_2255_50_314_34}