Definition:Constructible Point in Plane

Definition
Let $\CC$ be a Cartesian coordinate plane.

Let $S$ be a set of points in $\CC$.

Let $P$ be a point in $\CC$.

Let there exist a compass and straightedge construction for $P$ from a line segment $AB$, where $A, B \in S$

Then $P$ is defined as constructible from $S$.