QL-P15: 2^nd QL-Quasi Centroid

QL-P15 is the Centroid of the triangle formed by the three 2^nd 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 2^nd Quasi Centroid in a Quadrangle.

1^st 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)

1^st DT-coordinate

(m²-n²) (l⁴ – 3 l² m² + 3 l² n² + 5 m² n²)

Properties

• QL-P15 lies on this line:
  • QL-P8.QL-P12=QL-L8               (2 : 1)
• QL-P15 is the Reflection of QL-P14 (1^st 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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