The position vector of \(A\) is \(\begin{pmatrix}-1\\4\end{pmatrix}\). \(\overrightarrow{AB}=\begin{pmatrix}-3\\5\end{pmatrix}\).
Find the coordinates of \(B\).[1]
Find the equation of line \(AB\).[2]
\(C\) is the point \((-2,5)\). \(D\) is a point that lies on the line \(x=3\). The length of \(CD\) is 13 units. Find the two possible pairs of coordinates of \(D\).[3]
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Answer:(a)(i) \((-4,9)\) (a)(ii) \(y=-\frac53x+\frac73\) (b) \((3,-7)\) or \((3,17)\)