Show that the coordinates off the centroid of the triangle with vertices `A(x_1, y_1, z_1),\ B(x_2, y_2, z_2)a n d\ (x_3, y_3, z_3)` are `((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3,(z_1+z_2+z_3)/3)`

Explanation

Let D be the midpoint of BC. Join `A and D.`


Then, the coordinates of `D `are


`(x_2+x_3)/2, (y_2+y_3)/2, (z_2+z_3)/2`


Let G be the centroid of triangle ABC. Then, G lies on AD and divides it in the ratio `2:1`


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