Triangle $ABC$ has vertices $A(2, 2)$, $B(3, 5)$ and $C(4, 1)$. Triangle $A'B'C'$ has vertices $A'(-4, 4)$, $B'(-3, 7)$ and $C'(-2, 3)$. Write down the column vector for the translation that takes triangle $ABC$ to triangle $A'B'C'$.
$PQRS$ is a parallelogram. The position vector of $P$ relative to $O$ is $\overrightarrow{OP} = \begin{pmatrix}-4\\2\end{pmatrix}$. The position vector of $Q$ relative to $O$ is $\overrightarrow{OQ} = \begin{pmatrix}4\\6\end{pmatrix}$. Express $\overrightarrow{PQ}$ as a column vector.
Find $\overrightarrow{RS}$.
Find $|\overrightarrow{RS}|$.
The diagram shows triangle $D$. An enlargement with centre $(5, 4)$ and scale factor $2$ maps triangle $D$ onto triangle $E$. Draw and label triangle $E$.
An enlargement with centre $(5, 4)$ and scale factor $0.5$ maps triangle $D$ onto triangle $F$. Draw and label triangle $F$.
Triangle $G$ has vertices $(5, 4)$, $(4, 3)$ and $(3, 5)$. Triangle $F$ can be mapped onto triangle $G$ using a single enlargement. Triangle $F$ can also be mapped onto triangle $G$ using a different single transformation $T$. Describe fully the single transformation $T$.