2025 SJI PRELIMS P2 Q5

Line \(p\) is \(3x-2y=6\), line \(q\) is \(x+y=5\), and they intersect at \(T\).

1. Find \(T\).[3]
2. Line \(q\) meets the axes at \(A\) and \(B\). Find the shortest distance from the origin to \(AB\).[4]
3. \(O,B,R,T\) form a trapezium with \(OB\parallel RT\) and area 18 square units. Write down the two possible \(y\)-coordinates of \(R\).[3]