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Dans le repère orthonormé on donne les points A(−2; 7); B (2; 4); C(2; −1) et D(−2; 2) .
1. Faire une figure à compléter au fur et à mesure.
2. Calculer les coordonnées du milieu K du segment [AC].
3. Montrer que ABCD est un parallélogramme.
4. Calculer la distance AB.
5. On admet que AD=5. Que peut-on en déduire pour ABCD ?
6. Placer le point E tel que AEDK soit un parallélogramme. Lire ses coordonnées.
Bonus : Calculer les coordonnées de E.
7. Montrer que AEDK est un rectangle. (Aucun calcul supplémentaire n’est nécessaire).

Sagot :

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