# maximum distance in between points in taxicab metrics

Let's define distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ as $$|x_2-x_1| + |y_2-y_1|$$.

There are given some points.
I think how to find maximum distance between two arbitrary points (among given points). My inituition is following:
Let's find point $(x, y)$ such that $x+y$ is maximal and $(a, b)$ such that $a+b$ is minimal. I don't know idea about corectness. It is only intuition. Could you help me, please ?

Your idea as stated is incorrect. For example consider the points $$\{(-100,100),(100,-100),(1,1),(-1,1)\}$$