question_answer

The foot of the perpendicular from the point (2, 4) upon x + y = 4 is

A) (1, 3)    

B) (3, -1)

C) (2, 2)    

D) (4, 0)

Correct Answer: A

Solution :

[a]: From the figure let B is the foot of perpendicular so coordinates of B are (h,4-h).                   Slope of BA = \[\frac{4-4+h}{2-h}=\frac{h}{2-h}\] Slope of given line = -1. Since both the lines are perpendicular so \[\frac{h}{2-h}(-1)=(-1)\Rightarrow h=1\] \[\therefore \]Coordinates of foot of perpendicular are (1,3).