Geometry and complex numbers.
Geometry and complex numbers.
Exercise:
Prove that the medians of a triangle with vertices 
, 
and
intersect at the point
Solution:
Using the previous exercise we can write the medians of the triangle as
and
These segments intersect if and only if there are real numbers 
in the interval [0,1] such that
It's clear that 
is the unique
solution
to this system so the point of intersection is
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Author: Michael O'Neill