What is Manhattan Distance used to measure?

Manhattan Distance, also known as "taxicab" or "city block" distance, is specifically used to measure the distance between two points in a grid-based layout, emphasizing movement along axes rather than in a straight line. This distance is particularly relevant in scenarios where movement is constrained to a perpendicular grid, such as streets in a city where one can only travel along roads.

For example, in a city with a rectangular grid of streets, to get from one intersection to another, a person would have to travel along the streets, not through the buildings or in a diagonal line. Thus, Manhattan Distance takes the sum of the absolute differences of their Cartesian coordinates, which effectively accounts for the paths that are available given the obstacles in the direct line between the two points. This makes it particularly useful in urban planning, logistics, and various applications in Geographic Information Systems (GIS) where spatial analysis occurs on a grid framework.

The other choices refer to various forms of distance measurement but do not accurately represent the unique attributes and use cases of Manhattan Distance. It is not focused on straight-line distances, parallel lines, or three-dimensional contexts, but rather on situations where movement must navigate predetermined paths due to barriers.