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  4. A ray of light coming from the point (2,2 √3) is incident at an angle 30° 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:

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Q. 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:

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Solution:

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 $A (1, \sqrt{3})$
image
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