The points $ A\left(x_{1}, y_{1}\right), \mathrm{B}\left(x_{2}, y_{2}\right) $ and $ \mathrm{C}\left(x_{3}, y_{3}\right) $ are the vertices of $ \Delta \mathrm{ABC} $
What are the coordinates of the centroid of the triangle ABC?
Given:
The points \( A\left(x_{1}, y_{1}\right), \mathrm{B}\left(x_{2}, y_{2}\right) \) and \( \mathrm{C}\left(x_{3}, y_{3}\right) \) are the vertices of \( \Delta \mathrm{ABC} \)
To do:
We have to find the coordinates of the centroid of the triangle ABC.
Solution:
We know that,
Coordinates of the centroid of a triangle $=\left(\frac{\text { Sum of abscissa of all vertices, }}{3}, \frac{\text { Sum of ordinate of all vertices }}{3}\right)$
Therefore,
The coordinates of the centroid of the triangle ABC $=\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$
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