# 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 $\Delta \mathrm{ABC}$The median from $\mathrm{A}$ meets $\mathrm{BC}$ at $\mathrm{D}$. Find the coordinates of the point $\mathrm{D}$.

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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 $\Delta \mathrm{ABC}$
The median from $\mathrm{A}$ meets $\mathrm{BC}$ at $\mathrm{D}$.

To do:

We have to find the coordinates of the point $\mathrm{D}$.

Solution:

We know that,

The median bisects the line segment into two equal parts

$D$ is the mid-point of $B C$.

This implies,

Coordinate of mid-point of $B C=(\frac{x_{2}+x_{3}}{2}, \frac{y_{2}+y_{3}}{2})$

$D=(\frac{x_{2}+x_{3}}{2}, \frac{y_{2}+y_{3}}{2})$.

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