How do you find the furthest point away from a given location? (globally).?

Question

For instance, if I'm in a small village in Greenland, how would I find the literal furthest point away from that location (to the mile preferably) half way around the world.

Answer 1

The furthest point away from a place on the surface of the earth is its antipode.  The antipode is the point on the surface of earth where an arrow punched into a place and passing through the center of the earth would emerge on the opposite side of the globe. For North America most antipodal places are in the Indian Ocean

Answer 2

Easy.

Suppose you are at Nuuk (64 degree 10 minute 30 second N; 51 degree 44 minute 10 second W), then you take a point that is going to have the same latitude but expressed in degree SOUTH, and you add 180 degree to your longitude; hence 51:44:10+180 = 231:44:10. Because this value is larger than 180, you subtract from 360 to get the latitude East, hence 128 degree 15 minutes 50 second East. That is the point on the opposite of the world, in the Antarctic ocean, 2/3 of the way between Australia and the Antarctic cost.