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 co-ordinates of A

Answer 1

We know that the incident ray and the reflected ray equally inclined to the normal at A. Let A = (h, 0)

If AC makes an angle (-) with the normal at A, then it makes an angled (90° – θ) with positive x-axis and AB makes an angle (90° + θ) with positive x-axis. 

Now, slope of AB = tan (90° + θ) = – cot θ 

Slope of AC = tan (90° – θ) = cot θ 

∴ Slope of AB + slope of AC = θ