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

Explanation

From the law of reflection
`/_PAB=/_QAB`

`implies /_QAX=/_PAO`
Let `/_QAX=theta`
`:.tan theta="slope of"AQ`
`=(3-0)/(5-h)=(3)/(5-h)`……….`(1)`
Now, `/_PAX=18-0^(@)-/_PAO`
`=180^(@)-theta`
and `tan (18-0^(@)-theta)=`slope of `PA`
`implies -tan theta=(2-0)/(1-h)`
`implies (-3)/(5--h)=(2)/(1-h)` [From equation `(1)`]
`implies -3+3h=10-2h`
`implies 5h=13`
`h=(13)/(5)`
`:.` Coordinate of point `A=((13)/(5),0)`