A light ray emerging from the point source pl | vedclass

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(D) Let the abscissa of $Q$ be $x$.Since $Q$ lies on the $x$-axis,its coordinates are $Q(x, 0)$.Let the reflected ray make an angle $	heta$ with the

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$\frac{5}{2}$

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(D) Let the abscissa of $Q$ be $x$.Since $Q$ lies on the $x$-axis,its coordinates are $Q(x, 0)$.Let the reflected ray make an angle $	heta$ with the positive $x$-axis.The slope of the reflected ray $QR$ is $	an 	heta = \frac{7 - 0}{6 - x} = \frac{7}{6 - x}$.The incident ray $PQ$ makes an angle $(180^\circ - 	heta)$ with the positive $x$-axis.The slope of the incident ray $PQ$ is $	an(180^\circ - 	heta) = \frac{3 - 0}{1 - x} = \frac{3}{1 - x}$.Since $	an(180^\circ - 	heta) = -	an 	heta$,we have:$\frac{3}{1 - x} = -\left(\frac{7}{6 - x}ight)$$3(6 - x) = -7(1 - x)$$18 - 3x = -7 + 7x$$25 = 10x$$x = \frac{25}{10} = \frac{5}{2}$.

$A$ light ray emerging from the point source placed at $P(1, 3)$ is reflected at a point $Q$ on the $x$-axis. If the reflected ray passes through the point $R(6, 7)$,then the abscissa of $Q$ is

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