Polar coordinates

Question

While locating the polar coordinates of a point, why do we take the initial line as a directed line? Doesn't it suffice to mention that the angle that it makes will be measured with the positive direction of the $x$ axis?
Couldn't we just take a line segment?

Answer 1

To start off, I'd like to ask this : How do we define a vector completely?

We usually do so by defining three things.

1. It's sense
2. The angle it makes with a certain reference axis.
3. It's point of application

What I can infer is, you intend to ask that if we have defined the sense of the vector, why is there a need to specify the angle conventions, and vice versa.

I believe that the word directed segment itself implies that one of these things have to be defined. What the text means to say is that we take a segment, we measure the angle from the positive x, which makes the segment into a directed one.