**QL-12P1: A dozen of Equidistance Midpoints**

As described by lines QL-12L1 (Equidistance Lines Dozen) there are 12 lines per quadrilateral such that each line is separated by the 4 lines in 3 equal parts.

It is interesting that these 3 parts have a midpoint. It is in fact the midpoint of the part in the middle.

Since there are 4 equidistance lines per quadrigon of the Reference Quadrilateral there are also 4 Equidistance Midpoints per Quadrigon of the Reference Quadrilateral.

The 4 Equidistance Lines per Quadrigon are those lines where the middle segment of the Equidistance Line is the segment between the opposite lines.

*Coordinates:*The coordinates of the EquiDistance Midpoints are described in the paragraph of the EquiDistance Lines (QL-12L1).

*Properties:*- The 4 Equidistance Midpoints in a QL-Quadrigon lie on the corresponding Nine-point Conic (see QA-Co1) of the Quadrigon in question.
- The 4 Equidistance Midpoints in a QL-Quadrigon form a trapezoid, where

m3241.m4132 // m2134.m1243 // 3

^{rd}diagonal of the Quadrigon.- m3241.m2134 ^ m4132.m1243 = QG-P2 (midpoint 3
^{rd}diagonal of the Quadrigon). - Let L1, L2, L3, L4 be the lines of a Quadrigon where L1, L3 are opposite sides and L2, L4 are opposite sides. Let P be a point on the Nine-point Conic of the Quadrigon and let L be a line through P. When P is the midpoint of the line segment of L between L1 and L3 then P is automatically the midpoint of the line segment of L between L2 and L4.
- The Centroid of the 4 Equidistance Midpoints in a QL-Quadrigon lies on the Newton Line (see QL-L1).
- The Centroid of the 12 Equidistance Midpoints of all 3 QL-Quadrigons is a point also on the Newton Line (QL-L1).