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The triangle medians and the centroid.. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. . Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's cent
Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given ...
Typical left-hand motorway road layout in Ireland and South Africa Divided median strip on a boulevard in Huizhou, China. A median strip, central reservation, roadway median, or traffic median is the reserved area that separates opposing lanes of traffic on divided roadways such as divided highways, dual carriageways, freeways, and motorways.
Lines A, B and C are concurrent in Y. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil.
The three medians intersect each other at a point which is called the centroid of the triangle, which is its center of mass if it has uniform density; thus any line through a triangle's centroid and one of its vertices bisects the opposite side. The centroid is twice as close to the midpoint of any one side as it is to the opposite vertex.
In geometry, the Lemoine point, Grebe point or symmedian point is the intersection of the three symmedians (medians reflected at the associated angle bisectors) of a triangle. Ross Honsberger called its existence "one of the crown jewels of modern geometry". [1] In the Encyclopedia of Triangle Centers the symmedian point appears as the sixth ...
In the diagram, the medians (in black) intersect at the centroid G. Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, L . This point is called the triangle's symmedian point , or alternatively the Lemoine point or Grebe point .
For the 1-dimensional case, the geometric median coincides with the median.This is because the univariate median also minimizes the sum of distances from the points. (More precisely, if the points are p 1, ..., p n, in that order, the geometric median is the middle point (+) / if n is odd, but is not uniquely determined if n is even, when it can be any point in the line segment between the two ...