Question

What are the coordinates of the centroid of a triangle with vertices

P(−4, −1) , Q(2, 2) , and R(2, −3) ?

Answer 1

$\bf ~~~~~~~~\textit{Centroid of a Triangle}\\\\ \begin{array}{llll} P(x_1,y_1)\quad Q(x_2,y_2)\quad R(x_3,y_3)\\ \quad \\ \left(\cfrac{x_1+x_2+x_3}{3}\quad ,\cfrac{y_1+y_2+y_3}{3}\quad \right) \end{array} ~~ \begin{array}{llll} P(-4,-1)\quad Q(2,2)\quad R(2,-3)\\ \quad \\ \left(\cfrac{-4+2+2}{3}\quad ,\cfrac{-1+2-3}{3}\quad \right) \end{array}$

Answer 2

First let's find the lengths if the sides:
$PQ = 3 \sqrt{5} \\ pr = 2 \sqrt{13} \\ qr = 5$