Line segment

Segment definition

A line segment is a part of a line that is bounded by two distinct endpoints. It contains every point on the line between its endpoints. In geometry, a line segment is often denoted by its endpoints, for example, the line segment with endpoints A and B is denoted as \(\overline{AB}\).

Properties

A line segment has several important properties:

• **Length**: The distance between its two endpoints. This can be measured using the distance formula in a coordinate system.
• **Midpoint**: The point that divides the segment into two equal parts. The midpoint can be found using the midpoint formula.
• **Collinearity**: Any point on the line segment is collinear with the endpoints.

Types of Line Segments

Line segments can be classified based on their relative positions:

• **Horizontal Line Segment**: A line segment that runs from left to right or right to left.
• **Vertical Line Segment**: A line segment that runs up and down.
• **Oblique Line Segment**: A line segment that is neither horizontal nor vertical.

Applications

Line segments are fundamental in various fields of mathematics and engineering:

• In geometry, they are used to construct shapes and figures.
• In computer graphics, line segments are used to draw shapes and models.
• In physics, they can represent vectors and forces.

Related Concepts

• Line (geometry)
• Ray (geometry)
• Vector (mathematics and physics)
• Distance formula
• Midpoint formula
• Collinearity

See Also

• Geometry
• Coordinate system
• Euclidean space
• Vector space