I encouter a problem in complex analysis course :
Let $a, b, $ and $c$ be three distinct points on a straight line with $b$ between $a$ and $c$. Show that $\frac{a-b}{c-b} \in \mathbb{R}_{<0}$.
Precisely, I am not sure how to begin. Generally, I think that a point in complex plane $z = z + iy$ can be identified using coordinate $(x,y)$. But this seems does not make sence since I need to show that the ratio of different belongs to the set of negative real number, which is clearly in one dimension. Alternatively, I think that I might let $a = a_1 + ia_2, b = b = b_1 + i b_2$ and $c = c_1 + i c_2$. But I do not sure what form the straight line shold be. Is it $z_2 = az_1 + b$ where $z_1, z_2 \in \mathbb{C}$ and $a, b$ are complex constants? Please hint or give some useful suggestion. Thank you very much.