Problem 10 · 2022 Math Kangaroo
Medium
Geometry & Measurement
work-backward
The points A, B, C and D are marked on a straight line in this order as shown in the diagram. We know that A is 12 cm from C and that B is 18 cm from D. How far apart from each other are the midpoints of the line segments AB and CD?
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Answer: E — 15 cm
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Hint 1 of 2
Write the midpoints of AB and CD using the positions of the four points.
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Hint 2 of 2
The gap equals the average of AC and BD.
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Approach: midpoint distance = average of AC and BD
- Midpoint distance = ((C+D) − (A+B)) / 2 = ((C−A) + (D−B)) / 2.
- That is (AC + BD)/2 = (12 + 18)/2 = 15 cm.
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