Infinity Incorrect !
The longest distance between those two points is a straight line from one point , running all the way around the world to the second point.
Thus the shortest distance together with the longest distance is a full circle around the world with both points on the circle.
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867 miles
the distance between two points is length
You can never say, because the line could go on infinitely in any direction.
The metric of a geometric space is defined as the distance between two points.
The distance between these two points is termed as a wavelength.