Question

Find the coordinates of the centroid of the triange with the given vertices.

S(2,5) T(6,5) R(10,0)

Answer 1

`\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} S(x_1,y_1)\\ T(x_2,y_2)\\ R(x_3,y_3) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} S(2,5)\\ T(6,5)\\ R(10,0) \end{cases} \left(\cfrac{2+6+10}{3}~~,~~\cfrac{5+5+0}{3} \right)\implies \left(\cfrac{18}{3}~~,~~\cfrac{10}{3} \right)\implies \left( 6~~,~~3(1)/(3) \right)`