question_answer

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 \[R(5,10).\] The coordinates of Q are

A) \[(0,3)\]

B) \[(0,2)\]

C) \[(0,5)\]

D) None of these

Correct Answer: C

Solution :

[c] 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 \[{{P}_{1}}Q\] = Slope of \[{{P}_{1}}R\] or \[\frac{\lambda -3}{0-(-2)}=\frac{10-3}{5-(-2)}\] or \[\lambda -3=2\,\,or\,\,\lambda =5.\] Therefore, the point Q is (0, 5)