taxicab geometry

[jazziza87]

I have a question in my taxicab geometry section that reads like this:

The taxidistance between the points(x1,y1) and (x2,y2) in terms of x and y is d=..........? How would I find the formula for this problem? whever can help thanks alot. Also is it possible for there to be more than one minimum-distance path in taxicab geometry?

 

[pka]

The idea is: like a taxicab we must move only east & west or north & south.
So we have \(\displaystyle d = \left| {x_1 - x_2 } \right| + \left| {y_1 - y_2 } \right|\).

"Also is it possible for there to be more than one minimum-distance path in taxicab geometry?"
Yes. Ex. Go north and east or go east then north.