Derive the distance between two points formula

Question

Derive the distance between two points using Pythagorean Theorem

Answer 1

Pythagorean theorem

In a triangle ABC and it is right angled at B

AB = c and BC = a and AC = b

If b is the hypotenuse a and c are the sides

General form of finding distance is

If ABC is a triangle  right angled at B

A = (x1 , y1) and C=(x2 , y2)

Distance between AB = (x2 - x1) and between BC = (y2 - y1)and AC = d

From Pythagorean theorem

Therefore the formula for finding distance using Pythagorean theorem is