Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system ).
In two-and three-dimensional Euclidean space , the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem . The distance between the points (a,b) and (c,d) is given by (a -c) 2 + (b -d) 2 . In three dimensional space, the distance between the points (a, b, c) and (d, e, f) is (a -d) 2 + (b -e) 2 + (c -f) 2 .