QA-P1: QA-Centroid or Quadrangle Centroid
 
The Centroid of a Quadrangle is actually the center of gravity of a Quadrangle, replacing the points by equal masses.
The usual way to construct it is by connecting midpoints of opposite sides of a chosen component Quadrigon (see QG-1).
The two connecting lines as well as the line connecting the midpoints of the diagonals meet at the QA-Centroid.
 QA-P1-Centroid-00
However there is also another way to construct the Quadrangle Centroid using component triangles.
This way of construction makes it clear that it really is a Quadrangle Center because it can be constructed in the same way for all component triangles of the Quadrangle. 
This picture shows that the Centroid can be constructed by partitioning Gi.Pi in parts 3 : 1.
QA-P1-Centroid-00a
Coordinates: 
1st CT-Coordinate:
            2 p + q + r
1st DT-Coordinate:
            p2 (-p2 + q2 + r2)
 
 
Properties:
  • QA-P1 lies on these QG-lines:
 

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