[tex]A(2,-1); \quad B(-2,a) \\ \\ d_{AB}: \dfrac{x-x_A}{x_B-x_A} = \dfrac{y-y_A}{y_B-y_A}\ \Rightarrow \dfrac{x-2}{-2-2}= \dfrac{y-(-1)}{a-(-1)} \Rightarrow \\ \\ \Rightarrow \dfrac{x-2}{-4} = \dfrac{y+1}{a+1} \Rightarrow (a+1)(x-2) = -4(y+1) \Rightarrow \\ \\ \Rightarrow (a+1)x-2(a+1) = -4y-4 \Rightarrow (a+1)x - 2a-2 +4y+4 = 0 \Rightarrow \\ \\ \Rightarrow (a+1)x+4y-2a+2 = 0 \Rightarrow [/tex]
[tex]\Rightarrow d_{AB}: $ $ (a+1)\cdot x+4y-2a+2 = 0 \\ \\ \\\left\| \begin{array}{c} O(0,0) \in d_{AB} \\ $In d_{AB}$ inlocuim x=0, y=0 \end{array} \right| \Rightarrow (a+1)\cdot 0 +4\cdot 0-2a+2 = 0 \Rightarrow \\ \\ \Rightarrow -2a+2 = 0 \Rightarrow -2a = -2 \Rightarrow \boxed{a = 1}[/tex]
