Question

If a ray travelling along the line $x=1$ gets reflected from the line $x+y=1$, then the equation of the line along which the reflected ray travels is

• A. $y=0$
• B. $x-y=1$
• C. $x=0$
• D. none of these

Answer 1

The correct option is A $y=0$

Let $m$ be the gradient of the reflected ray.

The angle between $x=1$ and $x+y=1$ is ${45}^0.$

So the angle between the reflected ray and $x+y=1$ is also ${45}^0$

$\Rightarrow |\frac{m-(-1)}{1-m}|=\tan {45}^0=1\Rightarrow m+1=1-m\Rightarrow m=0$

So, the equation of the reflected ray is $y=0.$