How is an exact position in space identified?

Answer 1

There are several methods.

You need a reference point (the origin. For an n-dimensional space you will need a set of n axes and n measures which define the position with regard to origin. The axes need not be orthogonal (at right angles) as can be seen from isometric graph paper. The measures need not all be distances, they can comprise one distance and the remainder being angles.

Alternatively, you can have many reference points and directions from these reference points to the position. This is the system used by early cartographers for making maps before satellite mapping became possible. The reference points were called triangulation points, and as they moved across the region being mapped, they identified new triangulation points (whose positions they had worked out) so that they had these reference points reasonably near the position to be identified.

Yet another method was to have a set of reference points and distances from these reference points to the position. This is the system used for GPS where the reference points are 3 or more satellites and the measures are distances to the position. Actually, the measures are of time but given the speed of light in the Earth's atmosphere, converting time to distance is trivial. A lot of trigonometry follows.