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HW # 3 From Two Flowers to Three
Materials needed for this homework:
A copy of your hw
#2
Your reference
papers
Graph paper
(Don't have any? Get some
here)
Your compass
The definition of
perpendicular bisector and equidistant
The Pythagorean
Theorem
Your Book
1...... 2...... Get set.....Go. Plot the given coordinates for the flowers. Label each flower A, B, and C In your diagram, find all the possible locations, so that the flowers A and B get the same amount of water. Just like you did in "Only two Flowers" drawing a perpendicular bisector. Now, do the same for flowers A and C. Finally, do the same for B and C. Bingo! What did you notice? Where do those three perpendicular bisectors intercept? How many locations are there, so that the three flowers can get equally wet? Can you locate that point? Great! Now, help Leslie to place the sprinkler on that location. Here is how: Let's say that you are excited because you figure it out the location and you want to inform Leslie about your findings. Please give Leslie a clear and careful explanation of why the location -the point- that you choose works. (Please use as many math terms as possible in your explanation.) Lets' write Leslie an e-mail: Dear Leslie, I understood your dilemma in the case of only two flowers. Believe me, I have a dilemma of my own. But in this case, with three flowers, the location for the sprinkler is clear! Here is how I figured it out: ________________________________________________________ ________________________________________________________ ________________________________________________________ Based on my findings I strongly recommend that you place the sprinkler ..._______________________________________________ I am certain that this location will get the three flowers equally wet. Thank you for putting your trust in my math ability. Sincerely, Your name Here. Leslie read your e-mail and replied with the following e-mail. Dear student: I recognize all the effort that you put into this problem and for that I thank you. I am happy to inform you that your location works! All three flowers are receiving the same amount of water and they are growing equally beautiful. My neighbors were fascinated by your explanation but one of them keep asking me "how do you know that the distance from the sprinkler to each flower is exactly the same?" I do not know the answer to that. Can you help me one more time? Can you prove it mathematically? Sincerely, Leslie PS: I heard that a Greek philosopher named Pythagoras can help me, but I don't know that person. Moreover, he is from Samos and I do not know where that is! Can you tell me about him?Well, there you have it! Leslie is in trouble again and she needs your help. Why do you think she mentioned Pythagoras? Do you see any right triangle in your diagram? Do you know two sides of those right triangles? If so, she was right! Pythagoras can really help you.By the way, here is the Pythagorean Theorem: C2 = a2 + b2 Remember, you must prove, mathematically, that the distance between the sprinkler and the flowers are the same. In other words, that the triangles formed in your diagram are congruent. Do your calculation and be careful. Show ALL your work. After finishing with your calculations write back to Leslie. You can start you e-mail like this: Dear Leslie, Thanks for reminding me about Pythagoras. Yes, you were right! Pythagoras was a Greek philosopher from the city of Samoa. He discovered a way to find a missing side of a right triangle if you know the other two sides. His famous theorem states that: ___________________________________________ ___________________________________________ ___________________________________________ Which can be expressed by the following equation: C2 = a2 + b2 where a and b represent ______________________ and c represents ____________________________ I used his theorem to prove that the distance between the sprinkler and the flowers are the same. Here is how I did it: ___________________________________________ ___________________________________________ ___________________________________________ So, the distance between the sprinkler and the flowers are _____, proving, mathematically, that the three flowers will get equally wet. The flowers are equidistant from the sprinkler. Please share my calculations with your neighbor and let me know if he has more questions. I hope that your flowers turn out to be equally beautiful. Sincerely, Your name here.I am so proud of you! Now get all your papers organized and ready for tomorrow. Don't forget to share your work with your group.
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