Leibniz’s formula

Leibniz’s formula: Let G be the centroid of a set of points $(A_1, A_2, . . . , A_n )$ in the plane.

Then for any point M in the plane we have
$MA1_^2 + MA_2^2+· · ·+ MAn_^2 = n · MG^2 + GA_1^2 + GA_2^2 +· · ·+ GA_n^2$