I live in a city and, like most cities, it’s pretty much a grid. My daily destination is the exact opposite location of where I live. I was interested in knowing which method of walking will save me the most time, or if it matters at all?
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It doesn’t matter.
What you are talking about is called the [Manhattan Distance](https://en.wiktionary.org/wiki/Manhattan_distance) — also known as [Taxicab Geometry](https://en.wikipedia.org/wiki/Taxicab_geometry).
If you can only walk on grid lines, then it does not matter if you follow a zigzag pattern or all-the-way-down-then-all-the-way-across.
In practice, not all grid lines are the same. You should choose the path that is the easiest for walking — crosswalks that are less crowded and street crossings that don’t have long red lights.
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