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 2x−y+1=0,x+2y+3=0
By solving these equation we get foot of perpendicular as (−1,−1)