Geometry and complex numbers.

Exercise: Prove that the medians of a triangle with vertices tex2html_wrap_inline12 , tex2html_wrap_inline14 and tex2html_wrap_inline16 intersect at the point

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Solution:

Using the previous exercise we can write the medians of the triangle as

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and

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These segments intersect if and only if there are real numbers tex2html_wrap_inline26 in the interval [0,1] such that

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It's clear that tex2html_wrap_inline32 is the unique solution to this system so the point of intersection is

displaymath18

[Algebra] [Complex Variables]
[Geometry] [Trigonometry ]
[Calculus] [Differential Equations] [Matrix Algebra]

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Author: Michael O'Neill

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