The Euclidean distance is [math]d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}[/math]. The distinct between two points is exactly the length of the line segment that connects them.[br][br]The Taxicab metric on the Cartesian plane is [math]d_{taxi}\left(A,B\right)=\left|a-c\right|+\left|b-d\right|[/math]. This distance can be understood visually as the length of a shortest path taken between the two points that only moves horizontally or vertically.