Moving point in configuration of lines
Source: Iberoamerican 2018 Problem 3
September 26, 2018
analytic geometrycombinatoricscombinatorial geometry
Problem Statement
In a plane we have lines, no two of which are parallel or perpendicular, and no three of which are concurrent. A cartesian system of coordinates is chosen for the plane with one of the lines as the -axis. A point is located at the origin of the coordinate system and starts moving along the positive -axis with constant velocity. Whenever reaches the intersection of two lines, it continues along the line it just reached in the direction that increases its -coordinate. Show that it is possible to choose the system of coordinates in such a way that visits points from all lines.