Question

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

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

Answer 1

The correct option is D $(-1,-1)$

Let $Q(h,k)$ be the image of $O(0,0)$ w.r.t the line mirror $x+y+1=0$
$\frac{h-0}{1}=\frac{k-0}{1}=\frac{-2\left(1\right)}{2}$
$\Rightarrow h=k=-1$
$\Rightarrow h=-1,k=-1$
So, the image is at $(-1,-1)$