2025 CCHY PRELIMS P2 Q6

\(A\) is the point \((4,-2)\) and the line \(AB\) is parallel to the line \(\dfrac12x-3y=9\).

1. Find the equation of the line \(AB\).[2]
2. The equation of the line \(BC\) is \(2x+9y+52=0\). Find the \(x\)-coordinate of \(B\).[2]
3. It is given that \(\overrightarrow{AD}=\begin{pmatrix}3\\3\end{pmatrix}\) and \(\overrightarrow{AE}=\begin{pmatrix}5\\1\end{pmatrix}\).
   1. By considering their magnitudes, show that \(ADE\) is a right-angled triangle.[3]
   2. \(F\) is the point \((0,-6)\). Showing your working, determine if \(F\) lies on \(DA\) extended.[2]