intersecting line segments definition

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From Wikipedia

Line segment

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) 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).

Definition

If V\,\! is a vector space over \mathbb{R} or \mathbb{C}, and L\,\! is a subset of V,\,\! then L\,\! is a line segment if L\,\! can be parameterized as

L = \{ \mathbf{u}+t\mathbf{v} \mid t\in[0,1]\}

for some vectors \mathbf{u}, \mathbf{v} \in V\,\!, in which case the vectors \mathbf{u} and \mathbf{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

L = \{ \mathbf{u}+t\mathbf{v} \mid t\in(0,1)\}

for some vectors \mathbf{u}, \mathbf{v} \in V\,\!.

An alternative, equivalent, definition is as follows: A (closed) line segment is a convex hull of two points.

Properties

In proofs

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.

In an axiomatic treatment of Geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or else defined in terms of an isometry of a line (used as a coordinate system).

Segments play an important role in other theories. For example, a set is convex if the segment that joins any two points of the set is contained in the set. This is important because it transforms some of the analysis of convex sets to the analysis of a line segment.


Line segment intersection - Wikipedia, the free encyclopedia

ISBN 3-540-65620-0. Chapter 2: Line Segment Intersection, pp.19 44. ... For the simple case of testing the intersection of two line segments: Solution by ...


From Yahoo Answers

Question:it is said that a quadrilateral is formed by joining 4 line segments but a quadrilateral can also be formed by joining 4 lines(by intersecting them) then why only line segments is given or used in the definition of a quadrilateral?pls friends give me a answer fast it is very necessary

Answers:. Quadrilateral is a closed figure. Now if you wish to have a closed figure having four sides, these sides must be line segments. <<<<<<<<<<<<<<<<<<<<<< .

Question:Just wondering.

Answers:Yes, it's always a segment bisector.

Question:

Answers:A line segment is a part of a line that is bound by two distinct end points, and contains every point on the line between its endpoints.

Question:write the word that describes the lines or line segments. 1.the strings on a guitar 2.the marks left by a skidding car 3.sidewalks on opposite sides of a street 4.the segments that make up a + sign 5.the wires suspended between telephone poles 6.the hands of a clock at 9:00 P.M. 7the trunks of grown trees in a forest. please help. i dont understand this. :(

Answers:1) Parallel 2) Parallel 3) Parallel 4) Perpendicular 5) Parallel 6) Perpendicular 7) Parallel If the instructions are written as you wrote them, then it means pick the word that describes the relationship of the lines in each example. Like with the guitar strings or the sidewalk, these lines run in the same direction so they are parallel. Since a + sign has opposite lines, it is perpendicular, same with 9:00 because the hour hand is horizontal and the minute hand is vertical. Make sense?

From Youtube

Segment Intersection :demonstrations.wolfram.com The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Line segments are said to intersect when they cross each other. This can be determined mathematically by analyzing the endpoints of the line segments. Drag the endpoints to explore cases of intersecting line segments. In this Demonstration, the segments... Contributed by: Ed Pegg Jr

Lines and Segments that Intersect Circles :Learn about Lines and Segments that Intersect Circles