Find the equation

Given: equations are as follows:

3x + 2y + 6 = 0 … (1)

2x − 5y + 4 = 0 … (2)

x − 3y − 6 = 0 … (3)

Assuming:

In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.

Concept Used:

Point of intersection of two lines.

Explanation:

Solving (1) and (2):

x = −2, y = 0

Thus, AB and BC intersect at B (−2, 0).

Solving (1) and (3):

x = - 6/11, y = - 24/11

Thus, AB and CA intersect at

Similarly, solving (2) and (3):

x = −42, y = −16

Thus, BC and CA intersect at C (−42, −16).

Let D, E and F be the midpoints the sides BC, CA and AB, respectively. Then,

Then, we have:

Now, the equation of the median AD is

⇒ 16x – 59y – 120 = 0

The equation of the median BE is

⇒ 25x – 53y + 50 = 0

And, the equation of median CF is

⇒ 41 x – 112 y – 70 = 0