Question

In reperul cartezian xOy se considera punctele A (5, 2); B (-3, 7); C (1, -5).c) Calculati aria triunghiului ABC.

Answer 1

$A (5, 2); B (-3, 7); C (1, -5)\\\text{Putem folosi formula de calcul pentru aria triunghiului cu determinant.}\\\mathcal{A}=\frac{1}{2}\Delta, \text{ unde }\Delta= \left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|.\\\Delta= \left|\begin{array}{ccc}5&2&1\\-3&7&1\\1&-5&1\end{array}\right|=76\\\text{Deci: }\mathcal{A}=\frac{1}{2}76=38.$