What is the equation for working out the distance?

Answer 1

The answer depends on the metric being used.

With the "normal" Euclidian metric, the distance in 2-dimensional spance between the points (x1, y1) and (x2, y2) is sqrt[(x1 - x2)2 + (y1 - y2)2]. Analogous formulae can be used in spaces with 3 or more dimensions.

If using the Minkowski or Taxicam betric, the distance is |x1 - x2| + |y1 - y2|. This metric, also known as the Manhattan metric, is the sum of the differences in the x and the y coordinates. If you start from the corner of x1 avenue and y1 street in a grid (like Manhattan) and want to go to the corner of x2 avenue and y2 street and assuming you do not tunnel through buildings, the distance that you need to travel is the Minkovski distance.

There are many other metrics. In fact, there is a whole subject, within mathematics, called metric spaces!