Derive Distance Between Two Points Formula

This example demonstrates how to derive the distance between two points formula using the properties of a right triangle and Pythagorean's Theorem.

Steps

  1. Start with the formula for pythagorean theorem which relates the squares of the sides of the triangle together. We start here, because we can observe that a right triangle is formed between any two points in the Cartesian Coordinate Plane.

    Derive Distance Between Two Points Formula
  2. Then rearrange the formula so that is on the left side, which represents the distance we are solving for.

  3. Take the square root of both sides to isolate .

  4. Use the distance between two points in one-dimension to represent the length of .

  5. Use the distance between two points in one-dimension to represent the length of .

  6. Substitute the expressions of and into the equation.

  7. Finally replace the variable with to represent that derived formula represents the formula for the distance between two points 2d.