**In Real or Complex Vector Spaces**

If *V* is a vector space over or, and *L* is a subset of *V*, then *L* is a **line segment** if *L* can be parameterized as

for some vectors, in which case the vectors **u** and **u** + **v** are called the end points of *L*.

Sometimes one needs to distinguish between "open" and "closed" line segments. Then one defines a **closed line segment** as above, and an **open line segment** as a subset *L* that can be parametrized as

for some vectors .

Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points.

In geometry, it is sometimes defined that a point *B* is between two other points *A* and *C*, if the distance *AB* added to the distance *BC* is equal to the distance *AC*. Thus in the line segment with endpoints *A* = (*a _{x}*,

*a*) and

_{y}*C*= (

*c*,

_{x}*c*) is the following collection of points:

_{y}- .

Read more about this topic: Line Segment

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