question_answer

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                                                        [IIT 1970]

A)            \[x+2y=0\]                              

B)            \[2x+y=0\]

C)            \[x-y=0\]                                  

D)            None of these

Correct Answer: C

Solution :

           Since equation of diagonal \[11x+7y=9\]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.,\[x-y=0\].