QL-P15: 2nd QL-Quasi Centroid

 
QL-P15 is the Centroid of the triangle formed by the three 2nd Quasi Centroids (QG-P8) in a Reference Quadrilateral.
The prefix QL- has been added in the name of QL-P15 because there is also a 2nd Quasi Centroid in a Quadrangle.
 
 
 QL-P15 2nd QL-QuasiCentroid                      
Coordinates: 
1st CT-coordinate:
(m - n) (l5 m3 - 2 l4 m4 - l5 m2 n - 2 l4 m3 n + 6 l3 m4 n - l5 m n2 + 8 l4 m2 n2 - 9 l3 m3 n2 + l5 n3 - 2 l4 m n3 - 9 l3 m2 n3 + 20 l2 m3 n3 - 10 l m4 n3 - 2 l4 n4 + 6 l3 m n4 - 10 l m3 n4 + 6 m4 n4)
 
1st DT-coordinate:
(m2- n2) (l4 - 3 l2 m2 + 3 l2 n2 + 5 m2 n2)
 
 
Properties:
        QL-P8.QL-P12=QL-L8          (2 : 1)
  • QL-P15 is the Reflection of QL-P14 (1st QL-Quasi Centroid) in QL-P12 (Lateral Centroid).
  • QL-P15 is the Centroid of the Triangle formed by the 3 QL-versions of QG-P8 (note Eckart Schmidt).
  • QL-P15 is the Centroid of the Triangle formed by the 3 QL-versions of QG-P10 (note Eckart Schmidt).
  • QL-P15 is the Centroid of the Triangles formed by the 3 QL-versions of QG-P2, QG-P4, QG-P8 (all Centroid related points).
  • The 3 versions of QL-P15 in a Quadrangle are collinear.

 

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