Straight Line Question 130
Question: One vertex of the equilateral triangle with centroid at the origin and one side as $ x+y-2=0 $ is
Options:
A) $ (-1,-1) $
B) $ (2,2) $
C) $ (-2,-2) $
D)None of these
Correct Answer: C $ \Rightarrow \alpha =-\frac{h}{2},\beta =\frac{-k}{2} $ . Since $ (\alpha ,\beta ) $ lies on $ x+y-2=0 $
Þ $ \alpha +\beta -2=0 $ Show Answer
Answer:
Solution:
Þ $ \frac{k-0}{h-0}\times \frac{-1}{1}=-1\Rightarrow k=h $ …..(i) Let the coordinates of D be $ (\alpha ,\beta ) $ . Then the co-ordinates of O are $ ( \frac{2\alpha +h}{2+1},\frac{2\beta +k}{2+1} ) $ . Therefore $ \frac{2\alpha +h}{3}=0 $ and $ \frac{2\beta +k}{3}=0 $
Þ $ -h/2-k/2-2=0 $
Þ $ h+k+4=0 $
Þ $ 2h+4=0\Rightarrow h=k=-2 $ ,[from (i)] Hence the coordinates of vertex A are $ (-2,-2) $ .
BETA
