Answer to Question #135579 in Geometry for J

Question

Suppose that in a certain metric geometry satisfying Axioms D − 1 to
D − 3, points A, B, C, D are collinear and
AB = 4 = AC , BC = 6 , BD = 3 = CD , AD = 2
What betweenness relations follow? (Note: no ruler postulate, so use def.
of between)

Answer 1

BC = BD +CD therefore point D is between points B and C

AD=2 and AD<BD and AD<DC therefore point A is between points B and C

then BC=AB+AC = 4+4 =8

by the conditions of the problem BC=8, which is a contradiction

Therefore, this arrangement of points on one straight line is not possible

Answer :this arrangement of points according to the conditions of the task is impossible