Difference between revisions of "Centroid"
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| − | The '''centroid''' of a [[triangle]] is the point of intersection of the [[triangle | + | The '''centroid''' of a [[triangle]] is the point of intersection of the [[median of a triangle |medians]] of the triangle and is generally denoted <math>G</math>. 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. | ||
The coordinates of the centroid of a [[coordinatize]]d 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. | The coordinates of the centroid of a [[coordinatize]]d 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. | ||
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| − | + | <center>[[Image:centroid.PNG]]</center> | |
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== See also == | == See also == | ||
| + | * [[Cevian]] | ||
| + | * [[Geomtry]] | ||
Revision as of 11:11, 30 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 and is generally denoted 
. 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.
