What is a line segment, how many endpoints does it have, and how do you find its length and midpoint? A complete, diagram-based guide to one of geometry's most fundamental building blocks.
In geometry, a line segment is a straight path between two specific points, called endpoints. It includes every point that lies between those two endpoints, plus the endpoints themselves. Because it stops at both ends, a line segment has a definite, measurable length — unlike a full line, which never ends.
A line segment from point A to point B is written as segment AB, often shown with a small bar over the letters: A̅B̅. The order of the letters doesn't change the segment itself — segment AB and segment BA refer to the same set of points.
Figure 1: Line segment AB, bounded by two endpoints A and B, with a definite measurable length between them.
A line segment is best understood alongside the three other basic building blocks of geometry: the point, the line, and the ray. Together, these four concepts form the foundation for everything else in geometry.
Figure 2: A point marks a location, a line extends infinitely both ways, a line segment has two fixed endpoints, and a ray has one endpoint and extends infinitely in one direction.
| Concept | Endpoints | Length | Notation |
|---|---|---|---|
| Point | N/A (it is a location) | None — zero dimensions | Point P |
| Line | 0 (extends forever both ways) | Infinite / undefined | Line AB (with arrows), or ⟷AB |
| Line Segment | 2 (fixed start and end) | Fixed, measurable | Segment AB, or A̅B̅ |
| Ray | 1 (starts, never ends) | Infinite in one direction | Ray AB, or →AB (starts at A) |
This is one of the most searched questions on the topic: what is the difference between a line and a line segment? The answer comes down entirely to endpoints and length.
Extends infinitely in both directions. Has no endpoints and no measurable length. Drawn with arrowheads on both ends to show it continues forever.
A finite piece of a line, bounded by two endpoints. Has a fixed, measurable length. Drawn as a simple straight path with no arrowheads — it clearly stops at both ends.
Think of a line as an endless road with no beginning or end, while a line segment is like a single fence panel — it has a clear start, a clear finish, and you can measure exactly how long it is.
When a line segment's endpoints are placed on a coordinate plane, its length can be calculated precisely using the distance formula, which comes directly from the Pythagorean theorem.
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints
Figure 3: The line segment AB is the hypotenuse of a right triangle; the horizontal and vertical legs are the coordinate differences used in the distance formula.
Find the length of the line segment joining points A(2, 3) and B(6, 6).
SolutionLength = √[(6−2)² + (6−3)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5 units
The midpoint of a line segment is the point exactly halfway between its two endpoints, splitting the segment into two equal lengths.
Average the x-coordinates and average the y-coordinates separately
Find the midpoint of the line segment joining points A(2, 3) and B(6, 6).
SolutionMidpoint = ( (2+6)/2 , (3+6)/2 ) = ( 8/2 , 9/2 ) = (4, 4.5)
A perpendicular bisector is a line that crosses a line segment at exactly its midpoint, forming a 90° angle with it. It cuts the segment into two equal halves and, importantly, every point on the perpendicular bisector is the same distance from both endpoints of the original segment.
Figure 4: The perpendicular bisector crosses segment AB at a right angle, exactly at the midpoint M, where AM = MB.
Perpendicular bisectors are used throughout geometry — to construct the circumcenter of a triangle (the point equidistant from all three vertices), to find the center of a circle passing through given points, and in many compass-and-straightedge constructions.
Two line segments are called congruent when they have exactly the same length, regardless of their position or orientation in space. Congruent segments are marked with identical tick marks in diagrams to show they are equal without stating the exact measurement.
| Term | Meaning |
|---|---|
| Congruent line segments | Two or more segments with equal length, written as AB ≅ CD |
| Segment bisector | Any line, ray, or segment that passes through the midpoint of a segment, dividing it into two equal parts |
| Oblique line segment | A line segment that is neither horizontal nor vertical — it runs at a slant |
When two or more line segments or lines are drawn in the same plane, they can relate to each other in a few standard ways.
Lines or segments that never meet, no matter how far extended — they maintain a constant distance apart.
Lines or segments that intersect at exactly a 90° angle.
Lines or segments that cross each other at exactly one point, at any angle.
Lines that do not intersect and are not parallel — possible only in three-dimensional space, since they lie in different planes.
When two line segments meet at a point (called a vertex), they form an angle. Depending on the angle's measure, it is classified as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), or straight (exactly 180°) — all built from the same basic line segments covered in this article.
A line segment is a part of a line bounded by two distinct endpoints. Unlike a line, which extends infinitely in both directions, a line segment has a fixed, measurable length because it starts at one point and ends at another. It is one of the most basic building blocks in geometry, used to form the sides of shapes like triangles, squares, and polygons.
A line extends infinitely in both directions and has no endpoints, so it has no measurable length. A line segment is a finite portion of a line with two fixed endpoints, which gives it a definite, measurable length. In notation, a line through points A and B is written as line AB with arrows on both ends, while a line segment is written as segment AB with no arrows, since it stops at A and B.
A line segment has exactly two endpoints, one at each end, which define where the segment begins and ends. These two endpoints are what distinguish a line segment from a line, which has no endpoints, and from a ray, which has exactly one endpoint and extends infinitely in only one direction.
The length of a line segment with endpoints (x1, y1) and (x2, y2) on a coordinate plane is found using the distance formula: Length = square root of [(x2 − x1)^2 + (y2 − y1)^2]. This formula comes directly from the Pythagorean theorem, treating the horizontal and vertical differences between the two points as the legs of a right triangle and the line segment as the hypotenuse.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2). This formula finds the point exactly halfway between the two endpoints by averaging their x-coordinates and averaging their y-coordinates separately.
A perpendicular bisector of a line segment is a line (or line segment) that crosses the original segment at a 90-degree angle exactly at its midpoint, dividing it into two equal halves. Every point on a perpendicular bisector is equidistant from both endpoints of the original line segment, a property used frequently in geometric constructions and proofs.
A line extends infinitely in both directions with no endpoints. A line segment has two endpoints and a fixed, measurable length. A ray has exactly one endpoint and extends infinitely in only one direction, like a beam of light starting at a source. All three are made up of points and are fundamental concepts in geometry, but they differ in whether and how many endpoints they have.
