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Derivation of distance formula in 3 dimensions

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Write an essay of 1,000 words explaining how to derive the formula for the distance between two points in analytic geometry 3-space.
1. Describe all terms used as well as listing the steps.
2. Discuss how the Pythagorean theorem helps to find distances in 2 and 3 dimensions.
3. Apply the distance formula to real-life examples.
4. Include technology functions using a graphing calculator and computer software applications.
5. If you choose to use outside resources, include all in-text citations and references in APA format.

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