Question

A light ray emerging from the point source placed at P (2,3) is reflected at a point Q on the y-axis. If 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

Answer 1

The correct option is C $(0,5)$

In the above diagram, we have draw perpendicular on-axis from point $P$ so the point will be $P_1(-2,3)$

Now,

Slope od $P_{1}R=$ Slope of $PQ$

$\Rightarrow$ $\frac{10-3}{5+2}=\frac{\lambda -3}{0+2}$

$\Rightarrow$ $\frac{7}{7}=\frac{\lambda -3}{2}$

$\Rightarrow$ $1=\frac{\lambda -3}{2}$

$\Rightarrow$ $2=\lambda -3$

$\Rightarrow$ $\lambda =2+3$

$\Rightarrow$ $\lambda =5$

So, the co-ordinates of point $Q$ are $(0,\lambda )$ which is $(0,5)$