Question

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

Answer 1

With the given details, we can create a diagram.
Please refer to video for the diagram.
From the diagram, `/_PAD = /_QAC = theta`
Then, slope of `QA(m_1) = tan theta`
Slope of `PA(m_2) = tan (pi-theta) = - tantheta`
`:. m_1 = -m_2`
Let coordinates of point `A` is `(a,0)`. Then,
`(2-0)/(1-a) = -(3-0)/(5-a)`
`=>10-2a = 3a-3=>5a = 13=>a = 13/5`.
So,coordinates of point `A` are `(13/5,0)`.