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 $x+y-11=0\Longrightarrow\mathrm{A}$ .

2007 Cyprus MO, Lyceum (Problems)
Preceded by Problem 26	Followed by Problem 28
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2007 Cyprus MO/Lyceum/Problem 27

Problem

Solution

See also