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} $.

Academic Mathematics NCERT Class 10

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

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