Question

On a number line d(A,C)= 10 d (C.B) =8.Find d(A,B)considering all

possibilities?​

Answer 1

Step-by-step explanation:

Given, d(A, C) = 10, d(C, B) = 8. Case I: Points A, B, C are such that, A – B – C.

∴ d(A, C) = d(A, B) + d(B, C)

∴ 10 = d(A, B) + 8

∴ d(A, B) = 10 – 8

∴ d(A, B) = 2 Case II: Points A, B, C are such that, A – C – B.

∴ d(A, B) = d(A, C) + d(C, B) = 10 + 8

∴ d(A, B) = 18 Case III: Points A, B, C are such that, B – A – C. From the diagram, d(A, C) > d(B, C) Which is not possible

∴ Point A is not between B and C. ∴ d(A, B) = 2 or d(A, B) = 18.