- The triangle \(T\) has vertices \(A ( 2,1 ) , B ( 2,3 )\) and \(C ( 0,1 )\).
The triangle \(T ^ { \prime }\) is the image of \(T\) under the transformation represented by the matrix
$$\mathbf { P } = \left( \begin{array} { r r }
0 & 1
- 1 & 0
\end{array} \right)$$
- Find the coordinates of the vertices of \(T ^ { \prime }\)
- Describe fully the transformation represented by \(\mathbf { P }\)
The \(2 \times 2\) matrix \(\mathbf { Q }\) represents a reflection in the \(x\)-axis and the \(2 \times 2\) matrix \(\mathbf { R }\) represents a rotation through \(90 ^ { \circ }\) anticlockwise about the origin.
- Write down the matrix \(\mathbf { Q }\) and the matrix \(\mathbf { R }\)
- Find the matrix \(\mathbf { R Q }\)
- Give a full geometrical description of the single transformation represented by the answer to part (d).