# 2007 Cyprus MO/Lyceum/Problem 27

## Problem

In the diagram, the light beam $\epsilon$ is reflected on the $x$-axis and the beam $d$, being reflected on a mirror parallel to the $y$-axis at distance 6, intersects the $y$-axis at point $B$.
The equation of line $f$ is given by

$\mathrm{(A) \ } x+y-11=0\qquad \mathrm{(B) \ } x+y+11=0\qquad \mathrm{(C) \ } x-y+11=0\qquad \mathrm{(D) \ } x-y-11=0\qquad \mathrm{(E) \ } y=-x+10$

## Solution

The slope of $f$ is $-1$ and the distance $OB$ is $11$, so the equation is $y=-x+11$, or $x+y-11=0\Longrightarrow\mathrm{A}$.