Question

The coordinates of a point on the line $x+y+1=0$ which is at a distance $\frac{1}{5}$ unit from the line $3x+4y+2=0$ are

• A. $(2,-3)$
• B. $(-3,2)$
• C. $(0,-1)$
• D. $(-1,0)$

Answer 1

Answer: (B), (D)

The correct options are
B $(-3,2)$
D $(-1,0)$

Let the required points on the line $x+y+1=0$ be $(h,k)$

$k=-1-h$

Since the perpendicular distance of $(h,k)$ from the line $3x+4y+2=0$ is $\frac{1}{5}$,

$\frac{|3h+4k+2|}{\sqrt{3^2+4^2}}=\frac{1}{5}$

$\Rightarrow \frac{|3h+4(-1-h)+2|}{5}=\frac{1}{5}$

$\Rightarrow |3h-4-4h+2|=1$

$\Rightarrow |-h-2|=1$

$\Rightarrow -h-2=1or-h-2=-1$

$\therefore h=-3,-1$ and correspondingly $k=2,0$

The required points are $(-3,2)$ and $(-1,0)$