Leiame esmalt f(x) võrrandi:

$$f(x) = ax + b$$ $$f(3) = 3a + b = -2$$ $$f(-1) = -a + b = 4$$ $$\begin{cases} 3a + b = -2 \\ -a + b = 4 \end{cases}$$ $$-2-3a = 4 + a$$ $$-3a - a = 4 + 2$$ $$-4a = 6$$ $$a = -\frac{3}{2}$$ $$3(-\frac{3}{2}) + b = -2$$ $$-\frac{9}{2} + b = -2$$ $$b = \frac{5}{2}$$ $$y=-\frac{3}{2}x + \frac{5}{2}$$

Leiame g(x) võrrandi:

$$g(x) = cx + d$$ $$g(2) = 2c + d = 1$$ $$g(5) = 5c + d = 7$$ $$\begin{cases} 2c + d = 1 \\ 5c + d = 7 \end{cases}$$ $$1-2c = 7 - 5c$$ $$-2c + 5c = 7 - 1$$ $$3c = 6$$ $$c = 2$$ $$2*2 + d = 1$$ $$4 + d = 1$$ $$d = -3$$ $$y=2x - 3$$

Leiame lõikepunkti:

$$-\frac{3}{2}x + \frac{5}{2} = 2x - 3$$ $$-\frac{3}{2}x - 2x = -3 - \frac{5}{2}$$ $$-\frac{7}{2}x = -\frac{11}{2}$$ $$x = \frac{11}{7}$$ $$y = 2 \cdot \frac{11}{7} - 3 \newline = \frac{22}{7} - 3 \newline = \frac{22}{7} - \frac{21}{7} \newline = \frac{1}{7} $$

Leiame lõikepunkti kauguse punktist (0; 0):

$$\vec{AB} = \left( \frac{11}{7}; \frac{1}{7} \right) \newline AB = \sqrt{\left( \frac{11}{7} \right)^2 + \left( \frac{1}{7} \right)^2} \newline = \sqrt{\frac{121}{49} + \frac{1}{49}} \newline = \frac{\sqrt{122}}{7} $$