the sides of a quad taken at random are

x+3y-7=0 x-2y-5=0

3x+2y-7=0 7x-y+17=0

obtain the equation of the diagonals

Dear Abhishekh,

The lines intersect the x axis at a distance 7 , 5 , 7/3 , -17/7 
and the slopes of the lines are -1/3 , 1/2 , -3/2 ,  7
hence the sides taken in order are    x+3y-7 = 0
                                                          7x-y+17=0
                                                          3x+2y-7=0
                                                           x-2y-5=0
Solving the equations one by one we get their point of intersections.
and then making the equations of the diagonals we ge:-
1st Diagonal is 4x+5y-7=0,
Similarly the second Diagonal can be found.

Regards.