Two adjacent sides of a parallelogram are  4x + 5y = 0 and 7x + 2y = 0. If an equation to one of the diagonals is 11x + 7y – 9 = 0, then an equation of the other diagonal is

Since the given lines intersect at the origin O, one of the vertex is O (0, 0). Let A and B be the points of intersection of the sides 4x + 5y = 0 and  7x + 2y = 0 respectively with the diagonal. 11x + 7y – 9=0, then the coordinates of A and B are respectively 53,−43 and −23,73 the coordinates of the mid point of AB are 12,12. Since the other diagonalpasses through the vertex (0, 0) and the mid-point 12,12 of AB, its equation is y=x.