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

Answer 1

Answer: (B)

For point $A$
$\tan 60^{\circ }=\frac{2\sqrt{3}-k}{2-1}$
$\sqrt{3}=2\sqrt{3}-k$
$\therefore k=\sqrt{3}$
so point $A(1,\sqrt{3})$

Now slope of line $AB$ is $m_{AB}=\tan 120^{\circ }$
$m_{m_{AB}}=-\sqrt{3}$
Now equation of line $AB$ is
$y-\sqrt{3}=-\sqrt{3}(x-1)$
$\sqrt{3}x+y=2\sqrt{3}$
Now satisfy options