Question

The image of the point $(2,1)$ w.r.t. the line $x+1=0$ is:

• A. $(2,5)$
• B. $(0,5)$
• C. $(-4,1)$
• D. $(-2,-3)$

Answer 1

The correct option is C $(-4,1)$

Point $=(2,1)$, Line$:x+1=0$.

Let image $=(a,b)$
Equation of line $\perp$ to given line$:y=c$, where $c=$ constant
Now $(2,1)$ should lie on that line
So it should satisfy $y=c\Rightarrow 1=c$
Equation of that line$:y=1\Rightarrow b=1$
Also distance of $(2,1)$ from given line should be equal to distance of $(a,1)$ from given line
$\Rightarrow \frac{2+1}{\sqrt{1^2}}=-\frac{a+1}{\sqrt{1^2}}$

$\Rightarrow 3=-a-1$ or $a=-4$
So image is $(-4,1)$