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

Let the equation of sides AB and AD of the parallelogram ABCD be4x+5y=0----(1) and  7x+2y=0---(2)respectively. Solving (l) and (2), we have x = 0, y= 0 A = (0,0) Equation of one diagonal of the parallelogram is11x+7y=9---(3)Clearly, I (0, 0) does not lie on diagonal (3), therefore (3) is the equation of diagonal BD. Solving (1) and (3), we get B≡53,−43 and D≡−23,73 .  Since H is the middle point of BD∴H≡12,12 . Now the equation of diagonal AC which passes through A(0,0) and H12,12 is y−0=0−120−12(x−0) or  y−x=0