The coordinates of the vertices of a triangle are `(alpha_1 , beta_1) , (alpha_2 , beta_2)` and `(alpha_3 , beta_3)` Prove that the coordinates of its centroid are `(alpha_1 + alpha_2 + alpha_3)//(3)` ,` (beta_1 + beta_2 + beta_3)//(3)` .

Explanation

` therefore` the coordinates of C are
`(mx_2 + mx_1// m+n , my_2 + ny_1// m+n)`
= `( 2 (alpha_2 + alpha_3)/(2+1)+ 1. alpha_1 , 2(beta_2 + beta_3)/(2+1) + 1.beta_1)`
`((alpha_1 + alpha_2 + alpha_3)/3 , (beta_1 + beta_2 + beta_3)/3)`
which is the centroid of the triangle ABC.