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Betweenness

On a number l...

Question

On a number line, points A, B, and C are such that d(A, B) = 9 units, d(B, C) = 5 units, and d(A, C) = 4 units. Which of the points is between the other two?

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Solution

Given, d(A, B) = 9 .....(i)

d(B, C) + d(A, C) = 5 + 4 = 9...........(ii) [0.5 Marks]

$∴$ d(B, C) + d(A, C) = d(A, B) [From (i) and (ii)] [0.5 Marks]

Hence, point C is between point A and point B. [1 Mark]

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