Find the centroid of the triangle whose vertices are:

We know that the co-ordinates of the centroid of a triangle whose vertices are $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ is-

$\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$

(i) The co-ordinates of the centroid of a triangle whose vertices are (1, 4); (−1,−1); (3,−2) are-

$=\left(\frac{1-1+3}{3}, \frac{4-1-2}{3}\right)$

$=\left(1, \frac{1}{3}\right)$

(ii) The co-ordinates of the centroid of a triangle whose vertices are (−2, 3); (2,−1); (4, 0) are-

$=\left(\frac{2-2+4}{3}, \frac{3-1+0}{3}\right)$

$=\left(\frac{4}{3}, \frac{2}{3}\right)$