For 10 points, identify this point that is the intersection of the medians of a triangle.
The symmedian point is the isogonal conjugate of this point. For a finite set of points, this point minimizes the sum of the squares of the distances to them. The volume of a solid of revolution is equal to the area of the revolved figure times the distance traveled by this point according to Pappus's theorem. This point can be determined as the intersection of plumb lines formed by hanging this figure from two points. In a triangle, this point sits two-thirds of the way from any vertex to the opposite side, lies twice as far from the orthocenter as from the circumcenter, and its coordinates are the means of the vertex coordinates. For 10 points, identify this point that is the intersection of the medians of a triangle.
The symmedian point is the isogonal conjugate of this point.
centroid [or barycenter; or center of mass; prompt on center] &lt;Thompson&gt;