Difference between revisions of "Centroid"

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(changed inaccurate info - this would be much cleaner with a diagram, rather than stating these facts in unwieldy sentences.)
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The '''centroid''' of a [[triangle]] is the point of intersection of the [[median]]s of the triangle.  The centroid has the special property that, for each median, the distance from a vertex to the centroid is twice that of the centroid to the side.  Also, the three medians of a triangle divide it into six regions of equal area.
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The '''centroid''' of a [[triangle]] is the point of intersection of the [[median]]s of the triangle.  The centroid has the special property that, for each median, the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex.  Also, the three medians of a triangle divide it into six regions of equal area.
 
The centroid is the center of mass of the triangle; in other words, if you connected a string to the centroid of a triangle and held the other end of the string, the triangle would be level.
 
The centroid is the center of mass of the triangle; in other words, if you connected a string to the centroid of a triangle and held the other end of the string, the triangle would be level.
  

Revision as of 23:25, 10 July 2006

This article is a stub. Help us out by expanding it.

The centroid of a triangle is the point of intersection of the medians of the triangle. The centroid has the special property that, for each median, the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex. Also, the three medians of a triangle divide it into six regions of equal area. The centroid is the center of mass of the triangle; in other words, if you connected a string to the centroid of a triangle and held the other end of the string, the triangle would be level.

The coordinates of the centroid of a coordinatized triangle is (a,b), where a is the arithmetic average of the x-coordinates of the vertices of the triangle and b is the arithmetic average of the y-coordinates of the triangle.

(pictures needed)

(proofs of these properties anyone?)

(example problems?)


See also