## don't calculate vertices

ABC is a and the equation of the sides AB, BC, CA are
$a_1 x + b_1 y + c_1 = 0$ .... (1) $a_2 x + b_2 y + c_2 = 0$.... (2) $a_3 x + b_3 y + c_3 = 0$.... (3)

Find the eqn. of the medians of the triangle, without solving for the vertices.