2025 ESSS P2 Q8

The diagram shows a quadrilateral \(OABC\) with \(A(2p,p)\) and the length of \(OA\) is \(\sqrt{245}\) units.

\(AB\) is perpendicular to \(OA\) and \(B\) lies on the \(y\)-axis. \(N\) is the mid-point of \(AB\).

1. Show that \(p=7\).[2]
2. Calculate the gradient of \(OA\).[1]

It is given that \(C\) lies on the perpendicular bisector of \(AB\) and the equation of \(OC\) is \(y=-2x\).

3. Find the equation of \(AB\).[2]
4. Find the coordinates of \(C\).[4]
5. Find the area of quadrilateral \(OABC\).[2]