• On Finding the Shortest Distance of a Point From a Line: Which Method Do You Prefer?

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    • Keywords


      Shortest distance, mathematical methods, optimization, Lagrange multiplier.

    • Abstract


      The formula for the shortest distance of a point from a linecan be derived in several different ways. Some typical methodsare taught at the elementary (i.e., high-school and juniorcollege) level. However, solving such ‘school-book’ problemsusing advanced mathematical methods is often overlookedand neglected. This article illustrates how this formula canbe derived in various ways. Such a comparison will not onlyencourage the reader to explore and understand how andwhy mathematical techniques work, but it will also help understandthe common thread between different branches ofmathematics. This exercise also shows that ‘the best way’ tosolve a mathematical problem is a misnomer.

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