Question

A ray of light coming from the point $(2,2\sqrt{3})$ is incident at an angle ${30}^{\circ }$ on the line $x=1$ at the point $A.$ The ray gets reflected on the line $x=1$ and meets $X-$axis at the point $B.$ Then, the line $AB$ passes through the point:

• A. $(4,-\sqrt{3})$
• B. $(3,-\frac{1}{\sqrt{3}})$
• C. $(3,-\sqrt{3})$
• D. $(4,-\frac{\sqrt{3}}{2})$

Answer 1

The correct option is C $(3,-\sqrt{3})$


Equation of line $P^{\prime }B$ passing through $(0,2\sqrt{3})$
$(y-y_1)=m(x-x_1)$
$(y-2\sqrt{3})=\tan {120}^{\circ }(x-0)$
$y-2\sqrt{3}=-\sqrt{3}x$
$\sqrt{3}x+y=2\sqrt{3}$
In the given options, $(3,-\sqrt{3})$ satisfy the line.