Coordinate Geometry Question 90
Question: The orthocentre of the triangle with vertices (-2, -6), (-2, 4) and (1, 3) is
[J & K 2005]
Options:
A) (-3, 1)
B) (-1, 1/3)
C) (1, 3)
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ A(-2,-6),B(-2,4)C(1,3) $ be the vertices of the triangle. Slope of $ BC=\frac{3-4}{1+2}=\frac{-1}{3} $ Slope of $ \bot $ to $ BC=3 $ Equation of altitude through A is $ y+6=3(x+2) $
therefore $ y+6=3x+6 $
therefore $ y=3x $ …..(i) Slope of $ CA=\frac{3+6}{1+2}=\frac{9}{3}=3 $ Slope of $ \bot $ to $ CA=\frac{-1}{3} $ Equation of altitude through B is $ y-4=\frac{-1}{3}(x+2) $
therefore $ 3y-12=-x-2 $
therefore $ x+3y-10=0 $ …..(ii) Solving (i) and (ii) $ x=1,y=3 $
Hence, orthocentre (1, 3).
BETA
