question_answer

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

A) \[\left( \frac{1}{13},-\frac{1}{13} \right)\]

B)        \[\left( \frac{2}{5},-\frac{2}{5} \right)\]

C) \[\left( \frac{1}{3},-\frac{1}{3} \right)\]   

D)        None of these

Correct Answer: A

Solution :

[a]   Let A' be the image of \[A(2,3)\] on\[x+y=0\]. \[\Rightarrow \,\,\,\,\,\,\,A'\equiv \left( -3,-2 \right)\] 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 \[5x-8y-1=0.\] \[\Rightarrow \,\,\,B\equiv \left( \frac{1}{13},-\frac{1}{13} \right)\]