QL-P18: Reflection of QL-P8 in QL-P12

QL-P18 is the Reflection of QL-P8 in QL-P12.

Special about this point is that it lies on QL-L9, the M3D Line.

1^st CT-coordinate

l³ (m – n)² (m + n) – 2 l² (m² – n²)² – 2 m² n² (m² – m n + n²) + l m n (m + n) (4 m² – 7 m n + 4 n²)

1^st DT-coordinate

(m²-n²) (l² (l²+m²+n²) – 3 m²n²)

Properties

• QL-P18 lies on these lines:
  • QL-P8.QL-P12   = QL-L8                  (2 : -1 => P18 = Reflection of QL-P8 in QL-P12)
  • QL-P18.QL-P23 = QL-L9
• The 3 QA-versions of QL-P18 are collinear (note Eckart Schmidt).
• QL-P18 is the centroid of the three collinear points QG-P15 on QL-L9 (Eckart Schmidt, October 9, 2013). See [34], QFG # 286 and # 357.

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