Find the value of $|\overrightarrow{AC}|$.
$D$ is the point for which $\overrightarrow{AD} = \begin{pmatrix} 0 \\ k \end{pmatrix}$, where $k > 0$. $BD$ is parallel to $AC$. Show that $\overrightarrow{BD} = \begin{pmatrix} 6 \\ k - 11 \end{pmatrix}$.
Find the value of $k$.
Find how much the length of $AD$ differs from the length of $AC$.
Triangle $A$ has vertices $(\tfrac{1}{2}, 1)$, $(1, 2)$ and $(2, 2)$. Triangle $B$ has vertices $(-\tfrac{1}{2}, 1)$, $(-1, 2)$ and $(-2, 2)$. Describe fully the single transformation that takes triangle $A$ onto triangle $B$.
Triangle $A$ is mapped onto triangle $C$ by a transformation represented by the matrix $\begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix}$. Calculate the coordinates of the vertices of triangle $C$.
Find the matrix that represents the transformation mapping triangle $B$ onto triangle $C$.