Question 760292
I assume you are talking about using the Cartesian coordinate system with points a, b, c.  The a^2 + b^2 = c^2 is an application of the Pythagorean Theorem for right triangles.

Now each point has two values (x, y), so we write the distance between any two points as d = sqrt( (y2 - y1)^2 + (x2 -x1)^2 ).

There are many other coordinate systems where the shortest distance between two points is a curved line (ie Riemann Space).