Straight Lines: Foot of perpendicular MCQ

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Foot of perpendicularHardQuestion 300009

Question

The foot of perpendicular from (1, 0) to the line x + y = 2 is:

A
(3/2, 1/2)
Correct
B
(1, 1)
C
(2, 0)
D
(0, 2)

Correct answer

(3/2, 1/2)

Explanation

The perpendicular from (1,0) to x+y=2 has slope 1 (perpendicular to slope −1). Equation: y−0 = 1(x−1) → y = x−1. Substituting in x+y=2: x+(x−1)=2 → x=3/2, y=1/2. Foot = (3/2, 1/2).

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