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Distance formula

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The distance formula is a direct application of the Pythagorean Theorem in the setting of a Cartesian coordinate system. In the two-dimensional case, it says that the distance between two points P_1 = (x_1, y_1) and P_2 = (x_2, y_2) is given by d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}. In the n-dimensional case, the distance between (a_1,a_2,...,a_n) and (b_1,b_2,...,b_n) is \sqrt{(a_1-b_1)^2+(a_2-b_2)^2+\cdots+(a_n-b_n)^2}


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