# What Is a "Line Segment"?

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A line is a straight, one-dimensional geometrical figure that has no beginning or end and extends infinitely. It can pass through points but does not end at any point. A line is typically drawn with arrows on each end to demonstrate that it stretches to infinity. To break the line into pieces would create line segments, or parts of the line.

## Definition of a Line Segment

• A segment is a part or a piece of something larger. A line segment is a part of a line that connects two points, called endpoints. Like a line, a line segment is a one-dimensional geometric figure that has no width. Unlike a line, a line segment does not extend infinitely because it has a beginning and an end. Also unlike a line, the length of a line segment is measurable and quantifiable.

## Naming a Line Segment

• A line segment is identified by its endpoints, the points that mark its beginning and end. Endpoints are denoted with a capital letter, and the line segment is named for the two endpoints. The symbol for a line segment is the two capital letters with a dash over them. This denotes that it is not a line. To denote a line segment that is part of a polygon, like a triangle, a single, lower-case letter is used.

## Line Segments in Coordinate Geometry

• A line segment in coordinate geometry is similar to a line segment in ordinary plane geometry. In coordinate geometry, a line segment has a length that is measurable, begins and ends at endpoints, and the coordinates are on the coordinate plane. In ordinary plane geometry, the coordinates of the endpoints are unknown. A line segment in coordinate geometry is named for the endpoints, as in ordinary plane geometry.

## Midpoint of a Line Segment in Coordinate Geometry

• The midpoint of a line segment in coordinate geometry is exactly halfway between the two known endpoints of the line segment. This is also known as the Midpoint Theorem, which states that the midpoint's coordinates are the average of the coordinates of its endpoints; the x coordinate of the midpoint is the average of the x coordinates of the endpoints, and the y coordinate of the midpoint is the average of the y coordinates of the endpoints.

## References

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