Matrix representations of standard transformationsEdexcel International A Level Further Maths: Mind map

Exam questions on Matrix representations of standard transformations

1. Single transformations of the plane are represented by $2\times2$ matrices acting on position vectors, with the origin $O$ as the fixed point. The point $P$ has coordinates $(3,-2)$.
   The stretch parallel to the $x$-axis with scale factor $3$ maps $P$ to $P'$. Write down the matrix of the stretch and find the coordinates of $P'$.2 marks
2. The matrix $\mathbf{M}=\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ represents a single transformation $T$ of the plane.
   Show that $\mathbf{M}^2$ represents an enlargement, and state its centre and scale factor.2 marks
3. Triangle $T$ has vertices $A(1,1)$, $B(3,1)$ and $C(3,4)$.
   A rotation through $60^\circ$ anticlockwise about $O$ has matrix $\mathbf{R}$. Write down $\mathbf{R}$ with exact entries and find the exact coordinates of the image of $B$.3 marks