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Equidistant point (Posted on 2018-06-03) Difficulty: 3 of 5
Given a triangle ABC and a straight line L.

Find the point P on L such that
PA2+PB2+PC2 is the smallest.

No Solution Yet Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

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Solution final comment Comment 4 of 4 |
(In reply to re(2): one messy method by Steven Lord)

The answer makes sense. When A B and C are expressed in a coordinate system where L is the x-axis, their y distance contributions,

where d^2 = x^2 + y^2, being orthogonal to the line, are non-negotiable. Therefore their x distances alone are to be minimized, and this is done by choosing P to be located at their mean.  

  Posted by Steven Lord on 2018-06-05 12:49:05
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