2025 WGS P2 Q11

In the diagram below, \(ABCD\) is a quadrilateral where \(B\) is \((2,3)\), \(D\) is \((6,1)\) and \(A\) lies on the \(x\)-axis. \(AC\) is the perpendicular bisector of \(BD\), \(M\) is the mid-point of \(BD\) and \(CD\) is parallel to \(y\)-axis.

Find

1. the coordinates of \(M\),[2]
2. the equation of \(AC\),[4]
3. the coordinates of \(A\) and \(C\),[3]
4. the area of \(ABCD\).[2]