QA-P20: Reflection of QA-P5 in QA-P1


QA-P20 is the Reflection of QA-P5 (Isotomic Center) in QA-P1 (QA-Centroid).
                        
 
QA-P20-00
 
 
Coordinates:  
1st CT-coordinate:
            (q + r) (2 p + q + r) (p2 + p q + p r - q r)
1st DT-coordinate:
            1 / (-p2 + q2 + r2)

Properties:
  • QA-P20 lies on these QA-lines:
        QA-P1.QA-P5             (-1 : 2 => QA-P20 = Reflection of QA-P5 in QA-P1)
        QA-P3.QA-P29          ( 1 :  1 => QA-P20 = Reflection QA-P3 in QA-P29)
        QA-P11.QA-P37         (-1 : 2 => QA-P20 = Reflection of QA-P37 in QA-P11)
        QA-P21.QA-P31         (2 : -1 => QA-P20 = Reflection of QA-P21 in QA-P31)
        QG-P15.QG-P2          (2 : -1 => QA-P20 = Reflection of QG-P15 in QG-P2)
        QA-P34.QA-P35        (5 : -3)
  • QA-P20 is also he Reflection of:
        QA-P1 in QA-P22.
  • QA-P20 is the common point of these 3 lines:
L1= line parallel to M12.M34 through P1.P2 ^ P3.P4,
L2= line parallel to M13.M24 through P1.P3 ^ P2.P4,
L3= line parallel to M14.M23 through P1.P4 ^ P2.P3,
where Mij = midpoint(Pi,Pj) for (i,j) (1,2,3,4)
(Seiichi Kirikami, September 13, 2012).