A ray of light passing through the point A(1, | vedclass

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(A) Let the point $B$ be $(a, 0)$.Since the angle of incidence equals the angle of reflection,the slope of $AB$ is the negative of the slope of the re

Vedclass · Accepted Answer

$5x + 4y = 13$

Vedclass · Answer

(A) Let the point $B$ be $(a, 0)$.Since the angle of incidence equals the angle of reflection,the slope of $AB$ is the negative of the slope of the reflected ray $BC$ (where $C = (5, 3)$).The slope of $AB$ is $m_1 = \frac{0 - 2}{a - 1} = \frac{-2}{a - 1}$.The slope of $BC$ is $m_2 = \frac{3 - 0}{5 - a} = \frac{3}{5 - a}$.By the law of reflection,the angle with the normal (vertical line at $x=a$) is equal,implying the slopes satisfy $\frac{2}{a - 1} = \frac{3}{5 - a}$.$2(5 - a) = 3(a - 1)$ $\Rightarrow 10 - 2a = 3a - 3$ $\Rightarrow 5a = 13$ $\Rightarrow a = \frac{13}{5}$.Thus,$B = (\frac{13}{5}, 0)$.The slope of $AB$ is $m = \frac{0 - 2}{\frac{13}{5} - 1} = \frac{-2}{\frac{8}{5}} = -2 	imes \frac{5}{8} = -\frac{5}{4}$.The equation of line $AB$ is $y - 2 = -\frac{5}{4}(x - 1)$.$4(y - 2) = -5(x - 1)$ $\Rightarrow 4y - 8 = -5x + 5$ $\Rightarrow 5x + 4y = 13$.

$A$ ray of light passing through the point $A(1, 2)$ is reflected at a point $B$ on the $x$-axis and then passes through $(5, 3)$. Then the equation of $AB$ is:

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