2022 BTYSS P2 Q7

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

The coordinates of the points \(A\), \(B\) and \(C\) are \((2,-4)\), \((2a+2,a)\) and \((-3,1)\) respectively. The area of the triangle \(ABC\) is \(32.5\text{ units}^2\).

1. Given that \(a>0\), show that \(a=3\).[4]
2. Find the coordinates of the point when the line \(AC\) meets the \(x\)-axis.[3]
3. Find the equation of the perpendicular bisector of \(BC\).[4]