1963 AHSME Problems/Problem 37
Revision as of 17:53, 15 July 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 37 (credit to Arilato))
Problem
Given points on a straight line, in the order stated (not necessarily evenly spaced). Let be an arbitrarily selected point on the line and let be the sum of the undirected lengths . Then is smallest if and only if the point is:
Solution
By the Triangle Inequality, , with equality happening when is between and . Using similar logic, must be between and in order for the distance to be minimized.
The only point left to deal with is (which is also between and ). The minimum possible distance is (when is on ), so the answer is .
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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