Question 1203060
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Standard procedure to find the geometric center of any regular polygon given by coordinates of its vertices

is to find the mean arithmetic of  x-coordinates and the mean arithmetic of  y-coordinates, separately.


It works for regular triangles,  squares,  pentagons,  heptagons and all other regular  " n-gons ". 



In your case,  &nbsp;&nbsp;{{{x[center]}}} = {{{(-2+3+5+0)/4}}} = 1.5;  &nbsp;&nbsp;{{{y[center]}}} = {{{(2+4-1-3)/4}}} = 0.5.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>



It also works for arbitrary triangles, parallelograms, arbitrary quadrilaterals etc., when you look for the {{{highlight(centroid)}}} of the figure.



In addition to &nbsp;2D, &nbsp;it works in &nbsp;3D &nbsp;space for regular polyhedrons, &nbsp;too.



To learn more, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-triangle-is-the-Intersection-point-of-its-medians.lesson>The Centroid of a triangle is the Intersection point of its medians</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-parallelogram-is-the-Intersection-point-of-its-diagonals.lesson>The Centroid of a parallelogram is the Intersection point of its diagonals</A> 

in this site.