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Question
Points X, Y, Z are collinear such that d(X, Y) = 17, d(Y, Z) = 8, find d(X, Z).
Solution
Given, d(X, Y) = 17, d(Y, Z) = 8
Case I:
Points X, Y, Z are such that X – Y – Z.
∴ d(X, Z) = d(X, Y) + d(Y, Z)
∴ d(X, Z) = 17 + 8
∴ d(X, Z) = 25
Case II:
Points X, Y, Z are such that X – Z – Y.
∴ d(X, Y) = d(X, Z) + d(Z, Y)
∴ 17 = d(X, Z) + 8
∴ d(X, Z) = 17 – 8
∴ d(X, Z) = 9
∴ d(X, Z) = 25 or d(X, Z) = 9.
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