Question

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

• A. $x + 2 y = 0$
• B. $2 x + y = 0$
• C. $x - y = 0$
• D. None of these

Answer 1

Answer: (C)

$x - y = 0$

Answer 2

Since equation of diagonal $11 x + 7 y = 9$ does not pass through origin, so it cannot be the equation of the diagonal OB. Thus on solving the equation AC with the equations OA and OC, we get $A \left( \frac { 5 } { 3 } , - \frac { 4 } { 3 } \right)$ and $C \left( \frac { - 2 } { 3 } , \frac { 7 } { 3 } \right)$.

Therefore, the middle point M is $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$

Hence the equation of OB is $y = x$ i.e.,$x - y = 0$.