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Step 1:I'll solve this by providing a comprehensive explanation of the distance formula with proper LaTeX formatting:
Step 2:: Understanding the Distance Formula
The distance formula calculates the length between two points in a coordinate system. It is derived from the Pythagorean theorem and applies to two-dimensional (2D) and three-dimensional (3D) spaces.
Step 3:: 2D Distance Formula
d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}
Step 4:: 3D Distance Formula
d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} + (z_2 - z_1)^{2}}
Final Answer
The distance formula calculates the straight-line distance between two points by taking the square root of the sum of squared coordinate differences.
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