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 = (ax, ay) and C = (cx, cy) is the following collection of points:
- .
Read more about this topic: Line Segment
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