Find the equations of the medians of a triangle, the equations of whose sides are: `3x+2y+6=0,\ 2x-5y+4=0\ a n d\ x-3y-6=0`

Explanation

Given: 3x + 2y + 6 = 0 … (1)

2x − 5y + 4 = 0 … (2)
x − 3y − 6 = 0 … (3)
Let us assume, in triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.

Solving equations (1) and (2), we get x = −2, y = 0

Thus, AB and BC intersect at B (−2, 0).
Now, solving (1) and (3), we get x = – 6/11, y = – 24/11
Thus, AB and CA intersect at A (-6/11, -24/11)
Similarly, solving (2) and (3), we get x = −42, y = −16
Thus, BC and CA intersect at C (−42, −16).

Now, let D, E and F be the midpoints the sides BC, CA and AB, respectively. Then, we have:

D=(-22,-8) as it is mid points

E=(-234/11,-100/11)

F=(-14/11,-12/11)

Now, the equation of the median AD is

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