To review the Distance Formula between two points on the Cartesian Coordinate System (on the x-y coordinate system):
The "Distance Formula" tells us that the difference between two y-points squared added to the difference between two x-points squared will give us the square of the distance between x and y.
The formula tells us that if you get the difference between the 2 y-values and square that difference, get the difference between the 2 x-values and square that difference, then add these two differences together and finally, take their square root, you would arrive at the distance between the two points.
The distance formula looks like this: d-squared = (the difference in the y's squared) + (the difference in the x's squared).
Now it is beginning to look like the Pythagorean theorem of c squared = a squared + b squared.
The Pythagorean theorem of geometry states:
The square of the length of the hypotenuse of a right triangle = the sum of the squares of the lengths of the two shorter sides of the right triangle.
Or more succinctly stated: c squared = a squared + b squared. (c being the hypotenuse of a right triangle, a and b being the 2 shorter legs of that same right triangle.)
So, the distance formula is derived from the Pythagorean theorem. This makes it easier to remember, if we are familiar with the Pythagorean theorem.