A(6, 4), B(5, -2), C(7, -2) are the verteces of a isosceles triangle AB = AC
∆ ABC is a isosceles triangle, so the coordinates of D is \((\frac{5+7}{2},\frac{-2+-2}{2})=(6,-2)\) D(6, -2).
Length of AD = \(\sqrt{(6-6)^2+(4+2)^2}=6\)
Centroid divide AD in the ratio of 2 : 1
= \((\frac{18}{3},\frac{0}{3})\)
Centroid (6, 0)