2023 SCSS P2 Q9

Solutions to this question by accurate drawing will not be accepted.

The diagram shows a trapezium \(OABC\) in which \(OA\) is parallel to \(CB\). The coordinates of the point \(C\) are \((2,-4)\). The equation of the line \(BC\) is \(x=3y+14\).

1. Given that the point \(B\) lies on the \(x\)-axis, find the coordinates of \(B\).[1]

The point \(X\) lies on the line \(CB\) such that \(CX:XB\) is \(3:1\).

2. Find the coordinates of \(X\).[2]

The line through \(X\), perpendicular to \(CB\), passes through the point \(A\).

3. Find the coordinates of \(A\).[6]
4. Calculate the area of the trapezium \(OABC\).[3]