Question 46
The first quadrant of the Cartesian plane is the set of points $(x, y)$ with $x$ and $y$ strictly positive real numbers (i.e. $x\gt 0, y\gt 0$). Each point of the first quadrant is coloured red or blue. Moreover, for every point $P=(x, y)$ of the first quadrant, all points on the ray starting at $P$ with slope $y$ (i.e. the ray with origin $P$ passing through the point with coordinates $(x+1,2 y)$) have the same colour as $P$. Prove that all points of the first quadrant have the same colour.