Question

A ray of light is sent from the point $(1,4)$. Upon reaching the x- axis, the ray is reflected from the point $(3,0)$. This reflected ray is again reflected by the line $x+y=5$ and intersect y-axis at point P. Find the co-ordinate of P

• A. $\left(\frac{1}{2},0\right)$
• B. $\left(0,\frac{-1}{2}\right)$
• C. $\left(0,\frac{1}{3}\right)$
• D. $\left(2,\frac{1}{-2}\right)$

Answer 1

The correct option is B $\left(0,\frac{-1}{2}\right)$

$y-0=\frac{-4-0}{1-3}(x-3)$

$y=2(x-3)$

$2x-y-6=0$

$\therefore x+y=4$

$2x-y=6$

______________

$3x=11$

$x=11/3$

$y=5-11/3=4/3$

$\therefore \frac{x-3}{1}=\frac{y-0}{1}=2\frac{(3+0-5)}{2}\therefore y-2=-5/2$

$y=2-5/2=\frac{-1}{2}$

$x=5,y=2$

$y-2=\frac{4/3-2}{11/3-5}\times (x-5)$

$y-2=\frac{1}{2}(x-5)$ $\therefore y=(0,\frac{-1}{2})$