question_answer

The medians AD and BE of a triangle with vertices \[A\ (0,\ b),\ B\ (0,\ 0)\] and \[C\ (a,\ 0)\] are perpendicular to each other, if [Karnataka CET 2000]

A)            \[a=\sqrt{2}\ b\]                       

B)            \[a=-\sqrt{2}\ b\]

C)            Both (a) and (b)                        

D)            None of these

Correct Answer: C

Solution :

           From figure,            \[\left( \frac{b/2}{a/2} \right)\text{  }\left( \frac{b}{-a/2} \right)=-1\Rightarrow {{a}^{2}}=2{{b}^{2}}\Rightarrow a=\pm \sqrt{2}b\].