Question

The coordinates of the image of the origin O with respect to the straight line x+y+1=0 are

• A. $(-\frac{1}{2},-\frac{1}{2})$
• B. $(-2,-2)$
• C. $(1,1)$
• D. $(-1,-1)$

Answer 1

The correct option is D

$(-1,-1)$

Image of $(X_1,Y_1)$ w.r.to ax+by+c = 0 is (x,y) then

$\frac{x-X_1}{a}=\frac{y-Y_1}{b}=-\frac{2(a{X}_1+b{Y}_1+c)}{a^2+b^2}$

i.e., $\frac{x-0}{1}=\frac{y-0}{1}=\frac{-2\left(1\right)}{2}$ $\Rightarrow$ (x,y) = (-1,-1)