Answer :

Given:

A (−1, 6), B (−3, −9) and C (5, −8) be the coordinates of the given triangle.


Assuming:


D, E, and F be midpoints of BC, CA and AB, respectively. So, the coordinates of D, E and F are


To find:


The equation of median of a triangle.


Explanation:



Median AD passes through A (-1, 6) and D (1, -17/2)


So, its equation is


Formula used:



4y – 24 = -29x – 29


29x + 4y + 5 = 0


Median BE passes through B (-3,-9) and E (2,-1)


So, its equation is


Formula used:



5y + 45 = 8x + 24


8x – 5y – 21=0


Median CF passes through C (5,-8) and F(-2,-3/2)


So, its equation is


Formula used:



-14y – 112 = 13x – 65


13x + 14y + 47 = 0


Hence, the equation of line is 13x + 14y + 47 = 0


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