Question

A ray of light passing through the point (1, 2) reflects on the X-axis at a point A and the reflected
ray passes through the point (5,3). Find the coordinates of A
​

Answer 1

Answer:

Solution :

With the given details, we can create a diagram.

Please refer to video for the diagram.

From the diagram, ∠PAD=∠QAC=θ

Then, slope of QA(m1)=tanθ

Slope of PA(m2)=tan(π−θ)=−tanθ

∴m1=−m2

Let coordinates of point A is (a,0). Then,

2−01−a=−3−05−a

⇒10−2a=3a−3⇒5a=13⇒a=135.

So,coordinates of point A are (135,0).