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.
Let the coordinate of point A be (a, 0)
Draw a line (AL) perpendicular to the x –axis.
We know that angle of incidence is equal to angle of reflection. Hence, let
<BAL = <CAL = ɸ
Let <CAX = Ɵ
Therefore,
<OAB = 1800 –(Ɵ+2ɸ) = 1800 –[Ɵ+2(900 - Ɵ)]
= 1800 – Ɵ+1800 +2Ɵ
= Ɵ
Thus, <BAX = 1800 – Ɵ
Now, slope of line AC = 
------------ (1)
Slope of line AB = 
----------------- (2)
From equations (1) and (2), we get,
⇒ 3a – 3 = 10 – 2a
⇒ a = 
Therefore, the coordinates of point A are 
.
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