Abstract
The formula for the shortest distance of a point from a line can be derived in several different ways. Some typical methods are taught at the elementary (i.e., high-school and junior college) level. However, solving such ‘school-book’ problems using advanced mathematical methods is often overlooked and neglected. This article illustrates how this formula can be derived in various ways. Such a comparison will not only encourage the reader to explore and understand how and why mathematical techniques work, but it will also help understand the common thread between different branches of mathematics. This exercise also shows that ‘the best way’ to solve a mathematical problem is a misnomer.
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Suggested Reading
https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line.
S L Loney, The Elements of Coordinate Geometry–Cartesian Coordinates, G K Publisher, 2016.
Edwin K P Chong and Stanislaw H Zak, An Introduction to Optimization, Wiley India Private Limited, 2010.
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Gore, B.W. On finding the shortest distance of a point from a line: Which method do you prefer?. Reson 22, 705–714 (2017). https://doi.org/10.1007/s12045-017-0514-x
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DOI: https://doi.org/10.1007/s12045-017-0514-x