#### Question

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.

#### Solution

Let the coordinates 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 = *Φ*

Let ∠CAX = *θ*

∴∠OAB = 180° – (*θ* + 2*Φ*) = 180° – [*θ* + 2(90° – *θ*)]

= 180° – *θ* – 180° + 2*θ*

= *θ*

∴∠BAX = 180° – *θ*

Is there an error in this question or solution?

Solution 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. Concept: Distance of a Point from a Line.