Question

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

Options

• `(13/5, 0)`

• `(5/13, 0)`

• (–7, 0)

• None of these

Answer 1

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is `underlinebb((13/5, 0)`.

Explanation:

Let the co-ordinates of A be (a, 0).

Then the slope of the reflected ray is

`(3 - 0)/(5 - a)` = tan θ  (say)  ...(1)

Then the slope of the incident ray

= `(2 - 0)/(1 - a)` = tan(π – θ)  ...(2)

∵ tan θ + tan(π – θ) = 0

From (1) and (2)  

`\implies 3/(5 - a) + 2/(1 - a)` = 0

`\implies` 3 – 3a + 10 – 2a = 0

`\implies` a = `13/5`

Thus, the co-ordinates of A are `(13/5, 0)`.