Find the centroid of the triangle whose vertices are given by \$(1,10), (–7, 2)\$ and \$(–3, 7)\$.

Here \$(x_1, y_1) = (1, 10), (x_2, y_2) = (-7, 2)\$ and \$(x_3, y_3) = (-3, 7)\$.

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 + (-7) + (-3)}{3}, \frac{10 + 2 + 7}{3} ) \$

Add.

\$\Rightarrow ( - \frac{-9}{3}, \frac{19}{3} ) \$

Cancel out commmon factor.

\$ \Rightarrow (- \frac{\cancel{9} ^{3}}{\cancel{3} ^1}, \frac{19}{3} ) \$

Answer

The centroid of the triangle is \$ (- 3, \frac{19}{3}) \$.