The centroid of the triangle whose vertices are $(4,0),(0,-6)$ and $(2,6)$ is

$\begin{array}{l}LetA=(x_1,y_1)=(4,0),B=(x_2,y_2)=(0,-6),C=(x_3,y_3)=(2,6)\\ \therefore Thecentroid\\ G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})=(\frac{4+0+2}{3},\frac{0-6+6}{3})=(\frac{6}{3},\frac{0}{3})=(2,0)\end{array}$