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If 9 points X1, X2, …, X9 are chosen on a straight line in that order (but not necessarily evenly spaced), and Y is an arbitrary point on the line and S is the sum of the distances YX1, YX2, …, YX9, then S is minimized when the point Y is

midway between X2 and X8

at X9

at X5

midway between X4 and X6

midway between X1 and X9

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