# 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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