IAL 2025 May FP1 Q2

Question

[!problem]

The matrix $P$ represents the transformation $P$.

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

(a) Describe $P$ fully as a single geometrical transformation.

(2)

The matrix $Q$ represents the transformation $Q$.

$Q = \begin{pmatrix} -5 & 0 \\ 0 & 5 \end{pmatrix}$

(b) Describe $Q$ fully as a single geometrical transformation.

(2)

The transformation $R$ is a reflection in the line $y = -x$.

(c) Write down the matrix representing $R$.

(1)

The transformation $R$ maps the point $(4, 3)$ to the point $A$.

(d) Determine the coordinates of $A$.

(1)

The transformation $P$ followed by the transformation $Q$ maps the point $B$ to the point $A$.

(e) Determine the coordinates of $B$.

(2)