Question

The coordinates of the mid points of the sides of a triangle are (3, 1), (2, 3) and $(-2,2)$. Find the coordinates of the centroid of the triangle ABC.

Answer 1

Centroid of the triangle PQR and the Centroid of the triangle formed from the midpoints of the sides is the same.
Let the co-ordinate of the centroid of $\Delta ABC$ be (x, y) then
$(x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$
$=(\frac{3+2-2}{3},\frac{1+3+2}{3})=(1,2)$