Combined and inverse transformationsEdexcel International A Level Further Maths: Mind map

Exam questions on Combined and inverse transformations

1. The matrix $\mathbf{P}=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ represents a rotation through $90^\circ$ anticlockwise about $O$, and the matrix $\mathbf{Q}=\begin{pmatrix} 2 & 0 \\ 0 & 1 \end{pmatrix}$ represents a stretch parallel to the $x$-axis with scale factor $2$.
   Find the single matrix that represents $\mathbf{Q}$ followed by $\mathbf{P}$.2 marks
2. The matrix $\mathbf{M}=\begin{pmatrix} 4 & 3 \\ 2 & 2 \end{pmatrix}$ represents a transformation of the plane.
   A region of area $7\text{ cm}^2$ is transformed by $\mathbf{M}$. Find the area of its image.2 marks
3. A triangle $T$ has vertices $O(0,0)$, $A(2,0)$ and $B(0,3)$. The matrix $\mathbf{N}=\begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix}$ represents a transformation of the plane, and $T$ is mapped onto triangle $T'$.
   Find the coordinates of $A'$ and $B'$, the images of $A$ and $B$.3 marks