How is the distance formula like the pythagorean theorem explain?

The distance formula is simply a variation of the theorem. The method is the same with the Pythagorean however we are now dealing with 2 sets of points instead of 2 lengths. 

In the distance formula, the lengths are derived from the (x1,y1)->(x2,y2) coordinate points and the formula simplified. We still square the difference of x’s and difference of y’s to get our two squares then square root the sum to give our length. While the Pythagorean theorem is directly the sum of the square of the other two sides. 

Nevertheless, both formulas work on the same principle.