Straight Line Question 376

Question: The vertices of a triangle OBC are $ (0,\ 0),\ (-3,\ -1) $ and $ (-1,\ -3)\ $ respectively. Then the equation of line parallel to BC which is at $ \frac{1}{2} $ unit distant from origin and cuts OB and OC, is [IIT 1976]

Options:

A) $ 2x+2y+\sqrt{2}=0 $

B) $ 2x+2y-\sqrt{2}=0 $

C) $ 2x-2y+\sqrt{2}=0 $

D)None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • Gradient of $ BC=-1 $ and its equation is $ x+y+4=0 $ . Therefore the equation of line parallel to $ BC $ is $ x+y+\lambda =0 $ . Also it is $ \frac{1}{2} $ unit distant from origin. Thus $ \frac{\lambda }{\sqrt{2}}=\frac{1}{2}\Rightarrow \lambda =\frac{\sqrt{2}}{2}. $ Hence the required equation of line is $ 2x+2y+\sqrt{2}=0 $ .