A ray of light passing through the point A(2, 3) reflected at a point B on line `x + y = 0` and then passes through (5, 3). Then the coordinates of B are

Options

A. `((1)/(3),-(1)/(3))`
B. `((2)/(5),-(2)/(5))`
C. `((1)/(13),-(1)/(13))`
D. none of these

Answer

C

Explanation

Let A' is image of `A(2,3)` on `x +y = 0`
`rArr A' = (-3,-2)`
Now, B is the point of intersection of PA' with `x +y = 0`
Equation of line PA' is `y - 3 = (5//8) (x-5)` or `5x - 8y -1 = 0`

`rArr B -= ((1)/(13),-(1)/(13))`