Finding the length of a line (Distance Formula)

I've once heard a story on how Pythagoras came across his Pythagorean Theorem.

One day he was walking on a tiled floor, much like the image above. As he was looking at the pattern it formed, he noticed something amazing. The sum of the squares of the cathetus was equal to the square of the hypotenuse!

Or in mathematical terms: 

a² + b² = c²

But how is this tied to finding the length of a line?
This formula applies to all right-angled triangles, the same type of triangles drawn by the Cartesian coordinate system.

So if we have the length of the X and Y we calculate the length of the line like this:

h² = x² + y²  <=>  h = √( x² + y²)

But if we consider: 

x = x2 - x1

y = y2 - y1

Then the equation can be read like this (which is the distance formula):

 distance = √(( x2 - x1)² + ( y2 - y1)²)