Straight Line Question 123

Question: The coordinates of the foot of the perpendicular from the point (2, 3) on the line $ y=3x+4 $ are given by [MP PET 1984]

Options:

A) $ ( \frac{37}{10},-\frac{1}{10} ) $

B) $ ( -\frac{1}{10},\frac{37}{10} ) $

C) $ ( \frac{10}{37},-10 ) $

D) $ ( \frac{2}{3},-\frac{1}{3} ) $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ -y+3x+4=0 $ and perpendicular is $ \frac{y-3}{x-2}=\frac{-1}{3} $ or $ 3y+x-11=0 $ . Therefore foot is $ x=\frac{-1}{10},y=\frac{37}{10} $ .