4.01: Perpendicular bisector and reflection

0606/22/F/M/26 — Question 2 · 6 marks

Points \(A\) and \(B\) have coordinates \((1,3)\) and \((-7,1)\). The point \(P\) with coordinates \((2,a)\) lies on the perpendicular bisector of \(AB\).
(a)
Find the value of \(a\).
[4]
(b)
The point \(Q\) is the reflection of \(P\) in the line \(AB\). Find the coordinates of \(Q\).
[2]