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Question
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). Find the coordinates of the point A.
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Solution
Let the incident ray strike x-axis at the point A whose coordinates be (x, 0).
From the figure, the slope of the reflected ray is given by
tan θ = `3/(5 - x)` .....(1)
Again, the slope of the incident ray is given by
`tan(pi - theta) = (-2)/(x - 1)` (Why?)
or `- tan theta = (-2)/(x - 1)` ....(2)
Solving (1) and (2), we get
`3/(5 - x) = 2/(x - 1)` or x = `13/5`
Therefore, the required coordinates of the point A are `13/5, 0`.
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