Question

How do you derive the distance formula from Pythagorean theorem as a proof?

Answer 1

Do you know both the Pythagorean formula and the distance formula? If so, what mathematical operations would be needed to convert one into the other?

Answer 2

Think about this:
In the distance formula, you are using the change in x and change in y. You need to develop steps to show that those represent the sides of a right triangle. Once they are the sides of a right triangle, the Pythagorean applies.

Answer 3

Drawing a sketch and labeling it may be helpful.