Definition:Constructible Point in Plane

Definition
Let $\mathcal C$ be a Cartesian coordinate plane.

Let $P = \tuple {x, y}$ be a point in $\mathcal C$.

Let there exists a compass and straightedge construction for $P$ from the reference line segment joining $\tuple {0, 0}$ to $\tuple {1, 0}$.

Then $P$ is defined as constructible.