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.

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Solution

There are only two possibilities.
Case 1 : When point C is between the points A and B.

We have, d(A, C) = 10; d(C, B) = 8
Now, d(A, B) = d(A, C) + d(C, B) = 10 + 8
∴ d(A, B) = 18
Case 2 : When point B is between the points A and C.

We have, d(A, C) = 10; d(C, B) = 8
Now, d(A, C) = d(A, B) + d(B, C)
So, d(A, B) = d(A, C) − d(B, C) = 10 − 8
∴ d(A, B) = 2

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