2025 IGCSE 0580 May/June P22 Q9

\(A\) is the point \((3,-1)\).

\(\overrightarrow{AB}=\begin{pmatrix}2\\-4\end{pmatrix}\)

1. \(\overrightarrow{AC}=2\overrightarrow{AB}\)
   Find the coordinates of the point \(C\).[2]
2. The length of \(AB\) is \(k\sqrt5\).
   Find the value of \(k\).[2]
3. \(P\) is a point on \(AB\).
   \(AP:PB=1:3\)
   Find the position vector of \(P\).[2]