Given $n$ number of $(x, y)$ points, I want to find out which is the closest (linear distance) to the point of origin $(1, 1)$. Both $x$ and $y$ will always be positive integers.
Due to the magnitude of numbers I am dealing with, multiplication, division, square roots are out of the question. Due to this, Pythagorean theorem is out.
Adding, subtracting or comparing $x$ and $y$ will work but I'm not sure how to achieve this.
I do not want to calculate the actual distance using Pythagorean theorem. I just want to find out which of the points are the closest to the origin. Is there a way to determine this with the restrictions above?