Distance Formula in 2D and 3D and Their Proofs

In this video I prove the distance formula between 2 points in both two and three dimensions. The distance formula in 2D is readily derived using the Pythagorean theorem. In 3D we can extend the 2D distance formula by drawing a box and then applying the Pythagorean Theorem twice. Both distance formulas appear identical but with the 3D formula having the term in the z-axis. I also go over a quick example on calculating the distance between 2 points in 3D space.

The timestamps of key parts of the video are listed below:

- Distance Formula in 2D: 0:00
- Distance Formula in 3D: 1:49
- Example 4: 12:28

This video was taken from my earlier video listed below:

Related videos:

------------------------------------------------------

[mes]

This video was taken from my earlier video listed below:

[adamdobosz]

Thank you. I couldn't figure out how to derive this outside 2D. Good explanation.