Find the centroid of the triangle whose vertices are given by \$(–1, –3), (2, 1)\$ and \$(2, –4)\$.

Here \$(x_1, y_1) = (–1, –3), (x_2, y_2) = (2, 1)\$ and \$(x_3, y_3) = (2, –4)\$.

The centroid of the triangle is given by formula

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

Substiutute the values.

\$\Rightarrow ( \frac{(-1) + 2 + 2}{3}, \frac{(-3) + 1 + (-4)}{3} ) \$

Add.

\$\Rightarrow ( \frac{3}{3}, -\frac{6}{3} ) \$

Cancel out commmon factor.

\$ \Rightarrow ( \frac{\cancel{3} ^{1}}{\cancel{3} ^1}, - \frac{ \cancel{6} ^2}{\cancel{3} ^1} ) \$

Answer

The centroid of the triangle is \$ (1, -2) \$.