Straight Line Question 63

Question: 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]

Options:

A) $ a=\sqrt{2}\ b $

B) $ a=-\sqrt{2}\ b $

C)Both (a) and (b)

D)None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ ( \frac{b/2}{a/2} )\text{ }( \frac{b}{-a/2} )=-1\Rightarrow a^{2}=2b^{2}\Rightarrow a=\pm \sqrt{2}b $ .