Question

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

(A)  x + y = 0

(B)  x - y = 0

(C)  2x - 11y + 9 = 0

(D)  x - y - 9 = 0

Answer 1

Correct option  (B) x- y = 0

Explanation :

We have

4x + 5y = 0  .....(1)

7x + 2y = 0    ....(2)

11x +7y = 9   ......(3)

Solving Eqs.(1) and (2), we get

A = (5/3, -4/3)

Also solving Eqs. (2) and (3), we get

C = (-2/3, 7/3)

Now 

A(5/3, -4/3),O(0,0) and C(-2/3,7/3)

are three consecutive vertices of a paralleogram. The fourth vertex B is

(5/3 - 0 - 2/3, - 4/3 - 0 + 7/3) = (1,1)

Hence, the other diagonal is y = x