Question

Show that $D(-1,4,-3)$ is the centroid of $\Delta ABC$ with the vertices $A(3,2,-5),B(-3,8,-5)$ and $C(-3,2,1)$.

Answer 1

The vertices are $A(3,2,-5)B(-3,8,-5)C(-3,2,1)$

Centroid of Triangle is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})(\frac{3-3-3}{3},\frac{2+8+2}{3},\frac{-5-5+1}{3})(\frac{-3}{3},\frac{12}{3},\frac{-9}{3})=(-1,4,-3)$