2018 OIM Problems/Problem 3
Problem
In a plane we have 
lines without two being parallel, nor two perpendicular, nor three concurrent. A system of Cartesian axes is chosen with one of the straight lines as the axis of the abscissa. A point 
is located at the coordinate origin of the chosen system and begins to move at constant speed along the positive side of the 
-axis. Every time arrives at the intersection of two lines, continue along the line just reached in the direction that allows
the value of the abscissa of to always be always increasing. Show that you can choose the
Cartesian system axes so that passes through points of the lines.
Note: The abscissa axis of a plane coordinate system is the axis of the first coordinate or -axis.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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