Question

On a number line, points A, B and C are such that d(A,C) = 10, d(C,B) = 8. Find d(A,B) considering all possibilities.

Answer 1

Case 1: C lies between A and B. ie A-C-B


d(A,C) = 10
d(C,B) = 8
d(A,B) = d(A,C) + d(C,B)
d(A,B) = 10 + 8 = 18
Case 2: B lies between A and C. ie A-B-C


d(A,C) = 10
d(C,B) = 8
d(A,B) = d(A,C) - d(C,B)
d(A,B) = 10 - 8 = 2
Case 3: A lies between B and C. ie B-A-C
Since d(A,C) > d(C,B), A cannot lie in between B and C.