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

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

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{1 + 3 + 2}{3} ) \$

Add.

\$\Rightarrow ( \frac{1}{3}, \frac{6}{3} ) \$

Cancel out commmon factor.

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

Answer

The centroid of the triangle is \$ (\frac{1}{3}, 2) \$.