Find the equations of the medians of a triangle, the equations of whose sides are: 3x + 2y + 6 = 0, 2x – 5y + 4 = 0 and x – 3y – 6 = 0

Given:

   

   

And

   

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 have

   

   

Thus, AB and BC intersect at

   

Now, solving (1) and (3), we have

   

Thus, AB and CA intersect at

   

Similarly, solving (2) and (3), we get

   

Thus, BC and CA intersect at

   

Now,

let D, E and F be the midpoints the sides

BC, CA and AB, respectively.

Then, we have:

∴ The equations of the medians of a triangle are:

   

   

And,