Question

If the middle points of the sides of a triangle are $(1,1),(2,-3)$ and $(3,2)$, find the centroid of the triangle.

Answer 1

Let $A(1,1),B(2,-3),C(3,2)$ be the middle points of the sides of a triangle.

Here, $x_1=1,x_2=2,x_3=3$ and $y_1=1,y_2=-3,y_3=2$
Therefore $G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$=(\frac{1+2+3}{3},\frac{1-3+2}{3})$

$=(\frac{6}{3},\frac{0}{3})$

$G=(2,0)$