Distance Formula and Pythagorean Theorem. The distance formula is derived from the Pythagorean theorem. To find the distance between two points (x 1 ,y 1) and (x 2 ,y 2), all that you need to do is use the coordinates of these ordered pairs and apply the formula pictured below. The distance formula is. $ \text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2} $.