Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3,-9) and (5, -8).
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