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Be $m$ and $n$ two perpendicular lines, and be distinct points $A$ and $B$ outside the lines and in the first quadrant. What is the shortest way to get from point $A$ to point $B$ by tapping the two lines?

Idea: Listen say that the shortest path between a point and a line is perpendicular to this line, but I'm not convinced. =S

Danilo Santana
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  • To clarify, do you want to find two points, $P_m$ and $P_n$, such that the distance from $A$ to $B$, traveling through the other two points, is minimized, given the orientation of the lines and points? – SWilliams May 20 '15 at 13:32
  • $A$ and $B$ are in the same quadrant determined by $m$ and $n$? – Emilio Novati May 20 '15 at 13:33

1 Answers1

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Use reflections and the principle that the line segment is the shortest unrestricted path:

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Jack D'Aurizio
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