Difference between revisions of "Centroid"
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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. | 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. | ||
| − | The centroid is the center of mass of the triangle. | + | 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. | ||
(pictures needed) | (pictures needed) | ||
| + | |||
(proofs of these properties anyone?) | (proofs of these properties anyone?) | ||
| + | |||
(example problems?) | (example problems?) | ||
Revision as of 18:45, 10 July 2006
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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 centroid to the side. 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?)
