Points A, B, C, D and E are on the line (from left to right in that order). One of them is painted yellow, the other green, with a yellow dot to the left of the green one. The distance between A and C is 7 cm, between the yellow point and B is 8 cm, between the green point and D is 9 cm. Find the distance between the yellow and green points. Be sure to justify your answer.
Note that point A cannot be green, like the leftmost point, and E cannot be yellow, like the rightmost point.
From the condition “The distance between A and C is 7 cm, between the yellow point and B is 8 cm” it follows that A is not a yellow point, because the distance from A to B would be greater than the line segment AC that includes point B. For the same reason, point C is not a yellow point. And considering that B is neither a yellow nor a green point, we conclude that C cannot be a green point, because there should be a yellow dot to the left.
The only possible option is that point D is yellow, and E is green, because by condition, the yellow point lies to the left of the green one. The distance between them is 9 cm according to the condition.
Answer: 9 cm
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