Question

Find the centroids of the triangles whose vertices are given below.
(1) $(–7,6),(2,–2),(8,5)$

(2) $(3,–5),(4,3),(11,–4)$

(3) $(4,7),(8,4),(7,11)$

Answer 1

We know that, centroid of the triangle formed by the coordinates $A(x_1,y_1),B(x_2,y_2)$ and $A(x_3,y_3)$ is,

$G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

(1) $(–7,6),(2,–2),(8,5)$

The centroid of the triangle formed by the given coordinates is

$G_1=(\frac{-7+2+8}{3},\frac{6-2+5}{3})=(1,3)$

(2) $(3,–5),(4,3),(11,–4)$

The centroid of the triangle formed by the given coordinates is

$G_2=(\frac{3+4+11}{3},\frac{-5+3-4}{3})=(6,-2)$

(3) $(4,7),(8,4),(7,11)$

The centroid of the triangle formed by the given coordinates is

$G_3=(\frac{4+8+7}{3},\frac{7+4+11}{3})=(\frac{19}{3},\frac{22}{3})$