Question

In each of the following, decide whether the relation of betweenness exists among the points A, B and D. Name the point which lies between the other two.
(i) d(A,B) = 5, d(B,D) = 8, d(A,D) = 11
(ii) d(A,B) = 11, d(B,D) = 6, d(A,D) = 5
(iii) d(A,B) = 2, d(B,D) 15, d(A,D) = 17

Answer 1

(i) d(A,B) = 5, d(B,D) = 8 and d(A,D) = 11

We have,
d(A,D) $\ne$ d(A,B) + d(B,D)
d(A,B) $\ne$ d(A,D) + d(B,D)
d(B,D) $\ne$ d(A,B) + d(A,D)
Thus, there is no relation of betweenness among these three points.

(ii) d(A,B) = 11, d(B,D) = 6 and d(A,D) = 5

We have, 6 +5 =11
or d(A,B) = d(A,D) + d(D,B)
Thus, D is in between A and B, or A-D-B.

(iii) d(A,B) = 2, d(B,D) = 15 and d(A,D) = 17

We have, 2 + 15 = 17
or d(A,D) = d(A,B) + d(B,D)
Thus, B is in between A and D, or A-B-D.