2026 HGV P2 Q4

The diagram shows a quadrilateral \(ABCD\) in which the point \(B\) is \((0,3)\) and the point \(D\) is \((7,0)\). The equation of the line \(AD\) is \(5y=2x-14\) and \(C\) lies on the line \(y=x\). The line \(CD\) is parallel to the \(y\)-axis.

Given that \(A\) lies on the perpendicular bisector of \(BD\),

1. find the coordinates of \(A\) and of \(C\),[8]
2. find the area of the quadrilateral \(ABCD\).[2]