Q. 273.8( 4 Votes )

# 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.

Answer :

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 = 180^{0} –(Ɵ+2ɸ) = 180^{0} –[Ɵ+2(90^{0} - Ɵ)]

= 180^{0} – Ɵ+180^{0} +2Ɵ

= Ɵ

Thus, ∠BAX = 180^{0} – 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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