A light ray emerging from the point source placed at `P(2,3)` is reflected at a point `Q` on the y-axis. It then passes through the point `R(5,10)dot` The coordinates of `Q` are `(0,3)` (b) `(0,2)` `(0,5)` (d) none of these

Options

A. (0,3)
B. (0,2)
C. (0,5)
D. none of these

Answer

C

Explanation

The point of coincidence on the y-axis is `Q(0,lambda)`.
the image of `P(2,3)` on the y-axis is `P_1(-2,3)`.
`P_1,Q,` and R are collinear. Therefore, Slope of `P_1Q` =Slope of `P_1R`
or `(lambda-3)/(0-(-2))=(10-3)/(5-(-2))`
or `lambda-3=2`
or `lambda=5`
Therefore, the point Q is `(0,5)`.