Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve). If V is a vector space over R {displaystyle mathbb {R} } or C {displaystyle mathbb {C} } , and L is a subset of V, then L is a line segment if L can be parameterized as for some vectors u , v ∈ V {displaystyle mathbf {u} ,mathbf {v} in V,!} , 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 u , v ∈ V {displaystyle mathbf {u} ,mathbf {v} in V,!} . 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 R 2 {displaystyle mathbb {R} ^{2}} the line segment with endpoints A = (ax, ay) and C = (cx, cy) is the following collection of points: