The mid-point of A(2, 3) and B(6, – 5),
= \((\frac{2+6}{2},\frac{3-5}{2})=(4, -1)\)
And slope of AB, m =\(\frac{-5-3}{6-2}=-2\)
∴ Slope of the Perpendicular bisector of
AB, m’ = \(\frac{-1}{m}=\frac{1}{2}\).
Since the bisector passes through (4, – 1), so the equation of the Perpendicular bisector is
Y – (– 1) = \(\frac{1}{2}\)( – 4)
⇒ y + 1 = \(\frac{1}{2}\)(x − 4)
⇒ x – 4 = 2y + 2
⇒ x – 2y – 6 = 0, is the required equation.