2025 CGSS PRELIMS P1 Q18

In the figure below, line \(L_1\) and line \(L_2\) cut the \(x\)-axis at \(P\) and \(R\) respectively. The equation of \(L_1\) is \(y=2x-8\). Angle \(PRQ\) is \(45^\circ\). \(PR\) is 9 units. Line \(L_2\) meets line \(L_1\) at \(Q\).

1. By finding the coordinates of \(R\), show that the equation of line \(L_2\) is \(y=-x-5\).[4]
2. Find the coordinates of \(Q\).[2]
3. Find the shortest distance from \(R\) to line \(PQ\).[3]