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

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Question

(A) Let the coordinates of point $A$ be $(a, 0)$.By the law of reflection,the point $(1, 2)$ and the point $(5, 3)$ are such that the reflection of $(

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let the coordinates of point $A$ be $(a, 0)$.By the law of reflection,the point $(1, 2)$ and the point $(5, 3)$ are such that the reflection of $(1, 2)$ across the $x$-axis,which is $(1, -2)$,lies on the line passing through $A$ and $(5, 3)$.The slope of the line passing through $(1, -2)$ and $(5, 3)$ is $m = \frac{3 - (-2)}{5 - 1} = \frac{5}{4}$.The equation of this line is $y - 3 = \frac{5}{4}(x - 5)$.To find the $x$-intercept (point $A$),set $y = 0$:$-3 = \frac{5}{4}(x - 5)$$-12 = 5x - 25$$5x = 13$$x = \frac{13}{5}$.Thus,the coordinates of point $A$ are $\left(\frac{13}{5}, 0\right)$.

$A$ ray of light passing through the point $(1, 2)$ reflects on the $x$-axis at point $A$ and the reflected ray passes through the point $(5, 3)$. Find the coordinates of $A$.

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