pointintersection.py

Created by math-pana72

Created on November 23, 2021

681 Bytes

u->(1et-2) et v->(2et1)

A(1;1)  B(-1;2)

on a trouver les equations cartésiennes
de d et d'

d=2x+y-3  d'=x-2y+5

POINT INTERSECTION

1  2=1*1-(-2)*2=1+4=5differentde0
-2 1

donc u-> et v-> ne sont pas colinéaires
et don d et d' ne sont pas paralleles
d et d' sont donc sécantes

on utilise la méthode de substitution

§ -2x-y+3=0 
§ -x+2y-5=0

<-->§ y=-2x+3
      -x+2(-2x+3)-5
      
<-->§ y=-2x+3
      -x-4x+6-5=0

<-->§ y=-2x+3
      -5x+1=0

<-->§ y=-2x+3
      -5x=-1 donc x=1/5

<-->§ y=-2x+3=-2*1/5+3=-2/5+3
                 =-2/5+15/5=13/5
      x=1/5

<-->§ x=1/5
      y=13/5
      
conclusion:d et d' se coupent en I(1/5;13/5)

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