Question

what is betweenness of the point A,B,C if d(AB)=6,(BP)=5(AD)=11?​

Answer 1

Step-by-step explanation:

(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:

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

We have,

d(A,D) ≠ d(A,B) + d(B,D)

d(A,B) ≠ d(A,D) + d(B,D)

d(B,D) ≠ 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.

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