2026 IGCSE Additional Mathematics February/March 0606/22 Q2

Points \(A\) and \(B\) have coordinates \((1,3)\) and \((-7,1)\).

The point \(P\) with coordinates \((2,a)\) lies on the perpendicular bisector of \(AB\).

1. Find the value of \(a\).[4]
2. The point \(Q\) is the reflection of \(P\) in the line \(AB\).
   Find the coordinates of \(Q\).[2]