IP3 Class Test (May 2025) Q11 (2023 ACSBR AM Prelim P2 Q5)

The diagram shows an isosceles triangle \(PQR\) on a coordinate plane.

The diagram shows an isosceles triangle \(PQR\) with vertices at \(P(0, k)\), \(Q(3, 9)\) and \(R(h, 6)\), where \(h\) and \(k\) are positive constants and \(h > k\).

1. Show that \(h + k = 12\).[3]
2. It is now given that \(h = 7\).
   The point \(S\) is such that \(PQRS\) is a kite. Given that \(S\) lies on the line \(21y = 7x - 8\), find the coordinates of \(S\).[4]
3. Find the area of the kite.[2]