Check: Taxicab Distance vs. Euclidean Distance
The taxicab metric
The Euclidean distance is . The distinct between two points is exactly the length of the line segment that connects them.
The Taxicab metric on the Cartesian plane is . This distance can be understood visually as the length of a shortest path taken between the two points that only moves horizontally or vertically.
The solid path from A to B is a taxicab path
Euclidean Distance
Find the Euclidean distance between and .
Taxicab distance
Find the taxicab distance between and .