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line_segment_by_points(s,A,B) indicates that s is the line segment from A to B.

line_segment_by_points(s,A,B), line_segment_by_points(s,P,Q) <=> (A=P and B=Q) or (A=Q and B=P)

Optionally, a line_segment can contain a third point, the "via point", which is used to specify whether the segment "goes to infinity" or not; that is, line_segment(A,B,C) is the segment that starts at A, ends at B, and goes through C. C could be any point on the line which contains A and B. For instance; abusing notation, line_segment((0, 0), (0, 2), (0, 1)) would represent the ”normal segment" from (0, 0) to (0, 2), while line_segment ((0, 0), (0, 2), (0, 10)) would represent the segment that starts at (0, 0), goes to (0, -∞), and then continues from (0,∞) to (0, 2).


  1. line_segment example: source JSXGraph
  2. midpoint of line_segment example: source JSXGraph
  3. line_segment_by_infinity example: source JSXGraph