The distance from the origin to the image of $(1$, 1) with respect to the line $x+y+5=0$ is
The distance from the origin to the image of $(1$,
1) with respect to the line $x+y+5=0$ is
$7 \sqrt{2}$
$3 \sqrt{2}$
$6 \sqrt{2}$
$4 \sqrt{2}$
Solution
As we know that the image of $(1,1)$ with respect to line $x+y+5=0$ is
$\frac{x-1}{1}=\frac{y-1}{1}=\frac{2(1+1+5)}{1+1}$
$\Rightarrow x-1=-7, y-1=-7$
$\Rightarrow x=-6, y=-6$
$\therefore \quad$ Image of point $(1,1)$ is $(-6,-6)$ Now, distance from origin
This is the required transformed equation.
$D=\sqrt{(0+6)^2+(0+6)^2}$
$D=\sqrt{72}=6 \sqrt{2}$