Question

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

• A. $(1,-1)$
• B. $(-1,1)$
• C. $(1,1)$
• D. $(-1,-1)$

Answer 1

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
$x+2y+\mu =0\cdots \left(1\right)$
This line passes through a point $P(1,-2).$
On putting $x=1,y=-2$, we get $\mu =3$
$\therefore x+2y+3=0$
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 $(-1,-1)$