Symbol to denote the angle between two points

Question

Let $p = (0,0)$ and $q = (1,1)$ be two points. I would like to denote the angle between these two points ($45^\circ)$.

I took a look at the lists of symbols, and the symbols $\angle$ and $\measuredangle$ are used to denote angles, but usually when we have $3$ points (a triangle).

Is there any symbol to denote the angle between two points (in relation to the x-axis)?

Would $\measuredangle pq$ be wrong?

Answer 1

Two points do not determine an angle. You implied x-axis as a standard reference line.

Label or name the three points say $A,B,C$. Then $\measuredangle ABC $ is angle at the middle point B.

Answer 2

There is no symbol to denote the angle that a line defined by $p$ and $q$ makes with the x-axis because that's quite an arbitrary thing. We could measure the angle relative to any other line we want.

Instead, you could specify $X = (1,0)$ then say that $\angle q p X = 45^\circ$ and $\angle p q X = 135^\circ$.

Answer 3

In calculus you learn how to represent any point in $(\mathbb R \times \mathbb R) \setminus \{(0,0)\}$ with polar coordinates:

${\displaystyle x=r\cos \varphi }$
$ {\displaystyle y=r\sin \varphi }$

With the complex numbers, you see the same representation:

${\displaystyle z=re^{i\varphi }} $

For more, see Polar coordinate system.