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PROIECT PENTRU MATEMATICA

PROIECT PENTRU MATEMATICA. Eleva: Cotoban Valerica Clasa Xl C, Liceul G.S.I.A. CTA. APLICAŢII ALE DETERMINANŢILOR ÎN GEOMETRIE. Ecuatia unei drepte cand se cunosc 2 puncte distincte. TEOREMĂ

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PROIECT PENTRU MATEMATICA

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  1. PROIECT PENTRU MATEMATICA Eleva: Cotoban Valerica Clasa Xl C, Liceul G.S.I.A. CTA

  2. APLICAŢII ALE DETERMINANŢILOR ÎN GEOMETRIE

  3. Ecuatia unei drepte cand se cunosc 2 puncte distincte TEOREMĂ Fie punctele A (x1 , y1)şi B (x2 , y2). Atunci ecuaţia dreptei AB sub formă de determinant este:

  4. Exemplu 1: A(-1,2) ec.dreptei AB B(3,-1) x y 1 -1 2 1 3 -1 1 = = 2x+1+3y-6+y+x=3x-5+4y 3x+4y-5=0

  5. Exemplu 2: A(3,-4) ec.dreptei AB B(-2,5) x y 1 3 -4 1 -2 5 1 = =-x+15-2y-8x-3y-7=0

  6. Un punct M (x ,, y) aparţine unei drepte dacă coordonatele lui verifică ecuaţia dreptei. Consecinţă : Trei puncte A (x1 ,y1), B (x2 ,y2) şi C (x3,y3) sunt coliniare dacă şi numai dacă : Conditia de coliniaritate a 3 puncte

  7. Exemplu: A(-1,2) B(3,0) C(-2,1) Rezolvare: -1 2 1 3 0 1 -2 1 1 =0+3-4-0-6+1=-6

  8. Aria unui triunghi • A(x1,y1) • B(x2,y2) • C(x3,y3) x1 y1 1 x2 y2 1 x3 y3 1 = A=½

  9. Exemplu: A(-2,-3) B(-1,2) C(3,-1) -2 -3 1 -1 2 1 3 -1 1 = = -4+1-9-6-2-3=-14-6+2-3=-23 -2 -3 1 -1 2 1 A=½ -23 = ½ 23 = 23/2 x

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