In a rectangular coordinate plane,
M(10,25) represents the position of a factory.
N(34,7) represents the position of a workshop.
P is a point on x-axis which represents the position of a warehouse.
The goods produced from the factory MUST be first transported to workshop for good packaging by a truck.
Then, the packaged goods will be transported to the warehouse by the truck.
Afterthat, the truck needs to transport some raw materials from the warehouse back to the factory.
For the convenience of transport,straight roads MN, NP and PM are built.
Question: What is the minimum sum of the length of MN, NP and PM? Explain briefly.
The answer says the minimum sum of the length of MN, NP and PM is 70 units.But I don't know why.
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A very DIFFICULT math question
2008-06-21 12:53 am
回答 (2)
2008-06-21 1:33 am
✔ 最佳答案
The length of MN＝√[(34－10)²＋(25－7)²]＝√(24²＋18²)＝30As the length of MN is a constant, the sum of the length of MN, NP and PM is a minimum when NP＋PM is a minimum.
Consider the mirror image I(10,－25) of M about the x-axis, it is obvious that
PM＝PI
＝＞ NP＋PM＝NP＋PI
NP＋PM is a minimum when NP＋PI is a minimum, i.e. when I, P and N is colinear, and
the minimum of NP＋PM＝the minimum of NP＋PI＝NI＝√[(34－10)²＋(25＋7)²]＝√(24²＋32²)＝40
Therefore,
the minimum of MN＋NP＋PM＝30＋40＝70
2008-06-21 12:57 am
你沒有說明P在哪一點！
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