IsTim
  • IsTim
Triangle ABC is an equilateral triangle, with O as its centroid. Show that OA+OB+OC=0.
Mathematics
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IsTim
  • IsTim
Triangle ABC is an equilateral triangle, with O as its centroid. Show that OA+OB+OC=0.
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Hero
  • Hero
The distance is zero? How can that be?
IsTim
  • IsTim
|dw:1328767321746:dw|
IsTim
  • IsTim
That's what I think it looks like.

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Hero
  • Hero
Yeah, but distance is always positive so how can you add three positive distances and get zero?
IsTim
  • IsTim
|dw:1328767379548:dw|
Hero
  • Hero
Yes, you should post them as vectors.
IsTim
  • IsTim
|dw:1328767692094:dw|
Hero
  • Hero
I'll try to get an answer to this for you. No promises though
IsTim
  • IsTim
Thanks for trying then.
IsTim
  • IsTim
Uh. Hello?
Hero
  • Hero
I have your solution
Hero
  • Hero
1 Attachment
Hero
  • Hero
Any questions?
IsTim
  • IsTim
gimme a sec.
IsTim
  • IsTim
I don't seem to follow the process.
Hero
  • Hero
I'm sorry to hear that. I thought it would have been obvious
IsTim
  • IsTim
Is there a specific order you did this from?
Hero
  • Hero
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
Hero
  • Hero
Any questions?
Hero
  • Hero
I'll take questions concerning specific steps you have questions on
IsTim
  • IsTim
I'm just interpreting it right now. I guess I'm good for now. Thanks.

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