Since we know that both the rays reflected and incident are equally inclined to the normal at A. Now, coordinates of A = (x, 0). If AR makes an angle q with the normal at A, then it forms an angle 90° + θ with the positive x-axis and AS forms an angle 90° – θ with the positive x-axis.
Now, slope of AR = tan(90° + θ) = – cotθ
and slope of AS = tan(90° – θ) = cotθ
∴ Slope of AS + slope of AR = 0
⇒

3−0

5−1x

+

0−2

x−1

= 0 ⇒

3

5−x

+

−2

x−1

= 0
⇒ 3(x – 1) + (–2) (5 – x) = 0 ⇒ 3x – 3 – 10 + 2x = 0 ⇒ 5x – 13 = 0
⇒ x =

13

5

∴ The co-ordinate of A is (

13

5

,0).