Question

Question 24

What are the coordinates of the centroid of the triangle with vertices A(2, 4), B(3,-2), and C(-4, 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} A(\stackrel{x_1}{2},\stackrel{y_1}{4})\\ B(\stackrel{x_2}{3},\stackrel{y_2}{-2})\\ C(\stackrel{x_3}{-4},\stackrel{y_3}{0}) \end{cases} \\\\\\ \left(\cfrac{2+3-4}{3}~~,~~\cfrac{4-2+0}{3} \right)\implies \left( \cfrac{1}{3}~~,~~\cfrac{2}{3} \right)`