Q:

# What Is the 3-D Distance Formula?

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The 3D, or three-dimensional distance formula is the square root of the sum of the square of the difference between each coordinate point. In a three-dimensional plane, the coordinates are generally written with the variables x, y and z.

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The formula is the same as that for distance on a two-dimensional axis, but the three-dimensional formula uses three numbers in each coordinate rather than the two used to express two-dimensions. The same formula can be used to measure distance on a plane with any number of dimensions. The formula for distance on a multi-dimensional plane comes from Euclidean geometry and is derived from the Pythagorean Theorum, which is used to calculate the lengths of the side of a triangle.

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