QA-L3: QA-Centroids-Line


The QA-L3-Line is the line through the Centroid of the Quadrangle (QA-P1) and the Centroid of the Diagonal Triangle of the Quadrangle (QA-P10). It also passes through the Isotomic Center (QA-P5) and the 1st and 2nd QA-Quasi Centroids (QA-P25 and QA-P26).
Interestingly, all these points have coordinates independent of (a,b,c). As a consequence the coefficients of QA-L3 also are independent of (a,b,c).
Because the Centroid of the Quadrangle is on this line and it is divided in segments of fixed ratio this line has the allure of the Euler Line in Triangle environment.
QA-L3-Centroids-Line
                        
Coefficients: 
1st CT-coefficient:
p (q - r) / (2p + q + r)
1st DT-coefficient:
            (q2-r2) (-p2+q2+r2)
 
Properties:

 

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