Question

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5,3). Find the co-ordinates of the point A.

Answer 1

The image of the point P (1, 2) will be P’ (1, -2). 

Since ∠OAP = ∠XAQ (angle of inches = angle of reflection) 

So ∠OAP’ = ∠XAQ = a (Vertically opposite angles) 

⇒ P’, A, Q lie on a same line.

Now equation of the line P’, Q is [where P’ = (1, -2), Q = (5, 3)]

Since we find point of intersection with x axis we put y = 0.

So