QL-P14: 1st QL-Quasi Centroid

 
QL-P14 is the Centroid of the triangle formed by the three 1st Quasi Centroids (QG-P4) in a Reference Quadrilateral.
The prefix QL- has been added in the name of QL-P14 because there is also a 1st Quasi Centroid in a Quadrangle.
 
QL-P14 1st QL-QuasiCentroid          
Coordinates: 
1st CT-coordinate:
(m - n) (2 l5 m3 - 4 l4 m4 - 2 l5 m2 n - l4 m3 n + 9 l3 m4 n - 2 l5 m n2 + 10 l4 m2 n2 - 9 l3 m3 n2 - 3 l2 m4 n2 + 2 l5 n3 - l4 m n3 - 9 l3 m2 n3 + 13 l2 m3 n3 - 5 l m4 n3 - 4 l4 n4 + 9 l3 m n4 - 3 l2 m2 n4 - 5 l m3 n4 + 3 m4 n4)
 
1st DT-coordinate:
(m2- n2) (l4 + 3 l2 m2 + 3 l2 n2 - 7 m2 n2)
 
 
Properties:
        QL-P8.QL-P12 = QL-L8        (4 : -1)
  • QL-P14 is the Reflection of QL-P15 (2nd QL-Quasi Centroid) in QL-P12 (Lateral Centroid).
  • QL-P14 is the Centroid of the Triangle formed by the 3 QL-versions of QG-P4 (note Eckart Schmidt).

 

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