Problem

3. The triangle $T$ has vertices $A(2, 1)$, $B(2, 3)$ and $C(0, 1)$.

The triangle $T'$ is the image of $T$ under the transformation represented by the matrix

$P = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$

(a) Find the coordinates of the vertices of $T'$

(b) Describe fully the transformation represented by $P$

The $2 \times 2$ matrix $Q$ represents a reflection in the $x$-axis and the $2 \times 2$ matrix $R$ represents a rotation through $90°$ anticlockwise about the origin.

(c) Write down the matrix $Q$ and the matrix $R$

(d) Find the matrix $RQ$

(e) Give a full geometrical description of the single transformation represented by the answer to part (d).