Question

There are four points on a line: A, B, C and D, so that AB=1, BC=2, CD=4. Find all the possibilities of the length of segment AD.

Answer 1

{1, 3, 5, 7}

Explanation:

There are four possibilities:

AD = AB -BC -CD = 1 -2 -4 = -5

AD = AB +BC -CD = 1 +2 -4 = -1

AD = AB -BC +CD = 1 -2 +4 = 3

AD = AB +BC +CD = 1 +2 +4 = 7

Possible lengths of AD are 1, 3, 5, 7.

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The negative sign means the segment is added toward the left instead of toward the right. A final negative value means D is left of A, instead of to the right.