$\vec{AE} = \begin{pmatrix}6\\1\end{pmatrix}$. Calculate $|\vec{AE}|$.
$H$ is the midpoint of $AE$, and $\vec{FH} = \begin{pmatrix}2\\-3.5\end{pmatrix}$. Find $\vec{AF}$.
$G$ divides $BC$ in the ratio $1 : 2$. $\vec{BG} = \begin{pmatrix}2.5\\0\end{pmatrix}$ and $\vec{CD} = \begin{pmatrix}-1\\-7\end{pmatrix}$. Find $\vec{GD}$.
Explain why $GD$ is parallel to $FH$.
$B$ is the point $(3, 10)$. Find the coordinates of $D$.
Flag $A$ is mapped onto flag $T$ by the translation $\begin{pmatrix}-3\\-6\end{pmatrix}$. Draw, and label, flag $T$.
Describe fully the enlargement that will map flag $A$ onto flag $B$.
Find the centre of the rotation that will map flag $A$ onto flag $C$.
Rotate flag $B$ through $45^{\circ}$ anticlockwise about the origin. Label the image $R$.