A ray of light coming from the point (1, 2) i | vedclass

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Question

(A) Let $P = (1, 2)$ be the point from which the ray originates and $Q = (5, 3)$ be the point through which the reflected ray passes.Since the ray is

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$\left( \frac{13}{5}, 0 \right)$

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(A) Let $P = (1, 2)$ be the point from which the ray originates and $Q = (5, 3)$ be the point through which the reflected ray passes.Since the ray is reflected at point $A$ on the $x$-axis,the angle of incidence equals the angle of reflection.Let $R$ be the reflection of point $P(1, 2)$ across the $x$-axis. The coordinates of $R$ are $(1, -2)$.The reflected ray passes through $A$ and $Q$. Therefore,the points $R, A,$ and $Q$ are collinear.The equation of the line passing through $R(1, -2)$ and $Q(5, 3)$ is given by:$y - (-2) = \frac{3 - (-2)}{5 - 1}(x - 1)$$y + 2 = \frac{5}{4}(x - 1)$$4(y + 2) = 5(x - 1)$$4y + 8 = 5x - 5$$5x - 4y - 13 = 0$Point $A$ lies on the $x$-axis,so its $y$-coordinate is $0$. Substituting $y = 0$ into the equation:$5x - 4(0) - 13 = 0$$5x = 13$$x = \frac{13}{5}$Thus,the coordinates of point $A$ are $\left( \frac{13}{5}, 0 \right)$.

$A$ ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The coordinates of the point $A$ are:

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