[tex]A(-8;4) ,\quad B(-2,3), \quad C(4;-1), \quad D(a;b) \\ \\ $Ne folosim de vectori si observam din desenul din sistemul xOy ca:$ \\ \\ \overrightarrow{AD}} = \overrightarrow{BC} \Rightarrow (x_D-x_A)i + (y_D-y_A)j = (x_C - x_B)i + (y_C-y_B)j \Rightarrow \\ \\ \Rightarrow\Big(a-(-8)\Big)i+(b-4)j = \Big(4-(-2)\Big)i+(-1-3)j \Rightarrow \\ \Rightarrow (a+8)i+(b-4)j = 6i-4j [/tex]
[tex]\Rightarrow
\left\{ \begin{array}{c} a+8 = 6 \\ b-4 = -4 \end{array} \right \Rightarrow
\left\{ \begin{array}{c} a= 6-8 \\ b = -4+4 \end{array} \right \Rightarrow \left\{ \begin{array}{c} a= -2 \\ b = 0 \end{array} \right|\Rightarrow D(-2,0) [/tex]
