Difference between revisions of "Centroid"
(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]] | + | The '''centroid''' of a [[triangle]] is the point of intersection of the [[triangle median |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 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 10:46, 24 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?)
