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IsTim

  • 4 years ago

Triangle ABC is an equilateral triangle, with O as its centroid. Show that OA+OB+OC=0.

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  1. Hero
    • 4 years ago
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    The distance is zero? How can that be?

  2. IsTim
    • 4 years ago
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    |dw:1328767321746:dw|

  3. IsTim
    • 4 years ago
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    That's what I think it looks like.

  4. Hero
    • 4 years ago
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    Yeah, but distance is always positive so how can you add three positive distances and get zero?

  5. IsTim
    • 4 years ago
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    |dw:1328767379548:dw|

  6. Hero
    • 4 years ago
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    Yes, you should post them as vectors.

  7. IsTim
    • 4 years ago
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    |dw:1328767692094:dw|

  8. Hero
    • 4 years ago
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    I'll try to get an answer to this for you. No promises though

  9. IsTim
    • 4 years ago
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    Thanks for trying then.

  10. IsTim
    • 4 years ago
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    Uh. Hello?

  11. Hero
    • 4 years ago
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    I have your solution

  12. Hero
    • 4 years ago
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  13. Hero
    • 4 years ago
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    Any questions?

  14. IsTim
    • 4 years ago
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    gimme a sec.

  15. IsTim
    • 4 years ago
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    I don't seem to follow the process.

  16. Hero
    • 4 years ago
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    I'm sorry to hear that. I thought it would have been obvious

  17. IsTim
    • 4 years ago
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    Is there a specific order you did this from?

  18. Hero
    • 4 years ago
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    1. ABC is an equilateral Triangle 2. Segments OA, OB and OC are equidistant from the center 3. AB = BC = AC 4. AB, BC, and AC are labeled side s. 5. OA, OB and OC bisect angles A, B, and C. 6. OA bisects BC. 7. Create point D. 8. BD = -s/2 ; CD = s/2 9. x compnent OA = 0 because it's x component has no distance x compoent OB = -s/2 x component OC = s/2 10. x component 0 + s/2 - s/2 = 0 11. y component OB = s/2 tan(30) = -sqrt(3)/6 y component OB = y component OC = -sqrt(3)/6 12. y component OA = OA = OB 13. OB = s/2 cos(30) = s*sqrt(3)/3 14. y component OA + OB + OC = sqrt(3)/3 - sqrt(3)/6 - sqrt(3)/6 = 0 QED

  19. Hero
    • 4 years ago
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    Any questions?

  20. Hero
    • 4 years ago
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    I'll take questions concerning specific steps you have questions on

  21. IsTim
    • 4 years ago
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    I'm just interpreting it right now. I guess I'm good for now. Thanks.

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