Notes
line

Line and Line Segment

Line

A line in the plane is a non-empty set of points with the property that there is a vector, say $\vec{a}$, with the property that for any two points, say $P$ and $Q$, on the line then the position vector $\vec{P Q}$ is parallel to $\vec{a}$.

Line Segment

A line segment is a section of a line with the property that if $P$ and $Q$ are on the line then every point between $P$ and $Q$ on the line is also in the line segment.