QA-P31: Complement QA-P16 wrt QA-DT

MATHEMATICS

Chris van Tienhoven

QA-P31: Complement of QA-P16 wrt the Diagonal Triangle

QA-P31 is the complement of QA-P16 (QA-Harmonic Center) wrt the QA-Diagonal Triangle.

Coordinates:

1^st CT-Coordinate:

p (q + r) (2 p + q + r) (p² + p q + 2 q² + p r + q r + 2 r²)

1^st DT-Coordinate:

q² + r²

Properties:

– QA-P10.QA-P16 (-1 : 3 => QA-P31 = Complement QA-P16 wrt QA-DT)

– QA-P20.QA-P21 ( 1 : 1 => QA-P31 = Midpoint QA-P20.QA-P21)

QA-P31 = Midpoint QA-P16.QA-P19
QA-P31 is the Center of the parallelogram QA-P16.QA-P21.QA-P19.QA-P20.
QA-P31 is the QA-Centroid of the Quadrangle formed by the vertices of the QA-Diagonal Triangle and QA-P19.