# 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.

Let the coordinate 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 = ɸ

Let ∠CAX = Ɵ

Therefore,

∠OAB = 1800 –(Ɵ+2ɸ) = 1800 –[Ɵ+2(900 - Ɵ)]

= 1800 Ɵ+1800 +2Ɵ

= Ɵ

Thus, ∠BAX = 1800 Ɵ

Now, slope of line AC =

------------ (1)

Slope of line AB =

----------------- (2)

From equations (1) and (2), we get,

3a – 3 = 10 – 2a

a =

Therefore, the coordinates of point A are .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses