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:
- Vectors and the Geometry of Space: 3D Coordinate Systems:
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This video was taken from my earlier video listed below: