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Barycentric coordinates

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1. I'm struggling to follow the proof for the first question of the problems i.e. USAMO 2001/02. I'm not sure how they derived Q' + P = A + D2 for the y-coordinate. I understand how they derived the expression but not sure as to why it applys only to the y-coordinate and the bit about the Qz too, why is z-coordinate the ratio of z to y of P. Finally I don't get how Q is diametrically opposite to D1. Many thnx for any help.
2. (Original post by 11234)
I'm struggling to follow the proof for the first question of the problems i.e. USAMO 2001/02. I'm not sure how they derived Q' + P = A + D2 for the y-coordinate. I understand how they derived the expression but not sure as to why it applys only to the y-coordinate and the bit about the Qz too, why is z-coordinate the ratio of z to y of P. Finally I don't get how Q is diametrically opposite to D1. Many thnx for any help.
3. (Original post by RDKGames)
sorry
http://www.mit.edu/~evanchen/handout.../bary-full.pdf
4. (Original post by RDKGames)
do you have any tips for bmo2 especially barycentric and projective geometry
5. (Original post by 11234)
I'm struggling to follow the proof for the first question of the problems i.e. USAMO 2001/02. I'm not sure how they derived Q' + P = A + D2 for the y-coordinate. I understand how they derived the expression but not sure as to why it applys only to the y-coordinate and the bit about the Qz too, why is z-coordinate the ratio of z to y of P. Finally I don't get how Q is diametrically opposite to D1. Many thnx for any help.
The midpoint of Q'P is the midpoint of AD_2 as AQ' is of the same length as PD_2
6. (Original post by RichE)
The midpoint of Q'P is the midpoint of AD_2 as AQ' is of the same length as PD_2
ok but why equate y coordinates
7. (Original post by 11234)
ok but why equate y coordinates
Don't think it matters which co-ordinate the answer starts with. Each one is found in turn.

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