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Question

The coordinates of the foot of perpendicular drawn from the point (1,−2) on the line y=2x+1,is

A
(1,1)
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B
(1,1)
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C
(1,1)
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D
(1,1)
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Solution

The correct option is D (1,1)
Let M be the foot of perpendicular drawn from P(1,2) to y=2x+1. The equation of a line perpendicular to y=2x+1 is given by
x+2y+μ=0(1)
This line passes through a point P(1,2).
On putting x=1,y=2, we get μ=3
x+2y+3=0
Point M is the point of intersection of the lines 2xy+1=0,x+2y+3=0
By solving these equation we get foot of perpendicular as (1,1)

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