Savage Campos
05/09/2023 · High School
4. Soient \( \mathrm{P}, \mathrm{Q} \) les points milieux des diagonales d'un trapèze ABCD (orienté comme à la figure 1). Montrez que \( \overrightarrow{P Q}=\frac{1}{2}(\overrightarrow{A D}-\overrightarrow{B C}) \).
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Pour montrer que \( \overrightarrow{P Q} = \frac{1}{2}(\overrightarrow{A D} - \overrightarrow{B C}) \), on note \( P \) et \( Q \) les milieux des diagonales \( AC \) et \( BD \) d'un trapèze. On calcule les coordonnées de \( P \) et \( Q \) et montre que \( \overrightarrow{P Q} \) est égale à la moitié de la différence vectorielle entre \( \overrightarrow{A D} \) et \( \overrightarrow{B C} \).
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