# 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?

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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 $=\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$

Updated on 10-Oct-2022 13:28:51