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: https://youtu.be/xJ-qPJFf2gE
• Video notes: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems
• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiAJeLMzhOsrMliibfce5m .

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