Question

In reperul cartezian xOy se consideră punctele A(0,2) si B (8,6).Determinați coordonatele punctului C, stiind ca OABC estecparalelogram.​

Answer 1

$A(0, 2),\: B(8, 6),\: 0(0, 0),\: C(x_C, y_C)\\OABC\text{ paralelogram}\Leftrightarrow \text{ diagonalele } OB \text{ \c si } AC \text{ se \^injum\u at\u a\c tesc}\Leftrightarrow\\\Leftrightarrow \displaystyle\left \{ {{x_0+x_B=x_A+x_C} \atop {y_0+y_B=y_A+y_C}} \right. \Rightarrow \left \{ {{x_C=8} \atop {y_C=4}} \right. \Rightarrow C(8, 4)$