Find the centroid of the triangle whose vertices are the points \$(8, 4), (1,3)\$ and \$(3,–1)\$.

Here \$(x_1, y_1) = (8, 4), (x_2, y_2) = (1, 3)\$ and \$(x_3, y_3) = (3, -1)\$.

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{8 + 1 + 3}{3}, \frac{4 + 3 + (-1)}{3} ) \$

Add.

\$\Rightarrow ( \frac{12}{3}, \frac{6}{3} ) \$

Cancel out commmon factor.

\$ \Rightarrow (\frac{ \cancel{12} ^{4} }{ \cancel{3} ^{1}}, \frac{ \cancel{6} ^{2}}{\cancel{3} ^{1}}) \$

Answer

The centroid of the triangle is \$(4, 2)\$.