Question 192580
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I really wonder whether you really meant to say "the sum of the distances AM + BM is a <i>minimum,</i>" because what you have formed is a triangle with sides *[tex \large \overline{AM},\ \overline{BM},\ \overline{AB}].  The Triangle Inequality tells us that AM + BM must always be greater than AB, unless, of course, M is coincident with either A or B such that you no longer have a triangle and AM + BM = 0 + d = d or AM + BM = d + 0 = d -- such being the minimum limiting case.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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