Find the centroid of the triangle whose vertices are $A (4, - 6), B (3, - 2)$ and $C (5, 2)$

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Solution

The centroid $G (x, y)$ of a triangle whose vertices are
$(x_{1}, y_{1}) (x_{2}, y_{2}) (x_{3}, y_{3})$ is given by
$G (x, y) = G (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
We have $(x_{1}, y_{1}) = (4, - 6), (x_{2}, y_{2}) = (3, - 2), (x_{3}, y_{3}) = (5, 2)$
$∴$ The centroid of the triangle whose vertices are
$(4, - 6), (3, - 2)$ and $(5, 2)$ is
$G (x, y) = G (\frac{4 + 3 + 5}{3}, \frac{- 6 - 2 + 2}{3})$
$= G (4, - 2)$

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