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