demo1.py

Created by ramadiallo01

Created on December 10, 2021

615 Bytes

Propriété-définition 1. Le projeté
orthogonal H d’un point M sur une 
droite d est le point de d le plus 
proche de M. On dit que MH est la
distance de M à d.


Démonstration :       
- Si M∈(d) alors MH= et H est le 
point le plus proche de M
- Si M∉(d) alors il existe un point 
K tel que MK<MH
D'après le théorème de pythagore, 
dans le triange rectangle MHK, 
on a MK**2=MH**2+HK**2
D'après notre hypothèse, 
MH**2+HK**2<MH**2
on en déduit donc que HK**2<0
      absurde 
Donc il n'existe pas de point K
tel que MK<MH donc MH est la distance
la plus courte du point M à la droite (d)

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