Line Segment – Definition, Formula, Properties & Examples

The concept of line segment plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.

What Is a Line Segment?

A line segment is defined as a part of a straight line that is enclosed between two fixed points, called endpoints. It is different from a line (which goes on forever), and a ray (which has one endpoint and keeps going in one direction). A line segment has a definite length and can be measured. You’ll find this concept applied in geometry, coordinate systems, polygons, and even in real-world objects (like the edge of a ruler or the side of a book).

Line Segment vs Line vs Ray

Feature	Line	Line Segment	Ray
Length	Infinite	Finite, measurable	Infinite (in one direction)
Endpoints	No endpoints	2 endpoints	1 endpoint
Symbol	AB (with arrows on both ends)	AB̅ or \(\overline{AB}\)	\(\overrightarrow{AB}\)
Example	Road without end	Edge of a ruler	Sun’s ray

Line Segment Symbol and Naming

A line segment is named by its endpoints. For example, the segment joining point A to point B is written as AB̅ or \(\overline{AB}\). The bar above the letters shows it is a segment, not a line or ray.

• Common symbols: AB̅, CD̅, or \(\overline{PQ}\)
• Order of letters does not matter: \(\overline{AB}\) = \(\overline{BA}\)

Properties of Line Segments

• Has a fixed and measurable length
• Starts and ends at two distinct points (endpoints)
• Can be drawn, measured, and compared
• Forms the sides of polygons (triangles, rectangles, etc.)

Key Formula for Line Segment

When the coordinates of both endpoints are known, the length of a line segment can be determined using the distance formula:
\( \text{Length} = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \)
where (\(x_1, y_1\)) and (\(x_2, y_2\)) are the coordinates of the endpoints.

Cross-Disciplinary Usage

Line segments are important not just in Maths but also in Physics (for measuring distances and vectors), Computer Graphics (designing shapes), Engineering (construction drawing), and daily logical reasoning. Students preparing for JEE, NEET, or school olympiads will find this concept useful in various types of questions.

How to Measure a Line Segment

1. Place a ruler so that its zero mark aligns exactly with one endpoint of the segment.
2. Read the value on the ruler where the other endpoint falls—this is the segment’s length.
3. Record the length using the correct units (cm, mm, inches, etc.).

For maximum accuracy, use a divider along with the ruler. Put one leg of the divider at the first endpoint and the other at the second endpoint, then compare against the ruler scale.

Step-by-Step Illustration: Example Problem

Let’s find the length of a line segment joining P(3, 4) and Q(2, 0):

1. List coordinates: \( x_1 = 3,\, y_1 = 4;\, x_2 = 2,\, y_2 = 0 \)

2. Use the formula: \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

3. Substitute values: \( \sqrt{(2-3)^2 + (0-4)^2} = \sqrt{(-1)^2 + (-4)^2} \)

4. Calculate: \( \sqrt{1 + 16} = \sqrt{17} \approx 4.12 \) units

Final Answer: The segment PQ has length ≈ 4.12 units.

Line Segment in Figures and Real Life

• Sides of a triangle (AB, BC, CA)
• Edges of a rectangle or polygon
• Ruler’s edge
• Border of a book, mobile screen, or table top
• Road between two cities (on a simplified map)

Try These Yourself

• Draw a line segment of 8 cm using a ruler and label its endpoints.
• Find the length of the line segment joining (1, 2) and (5, 5).
• Name all line segments that can be formed from the vertices of a square.
• Draw and distinguish between a line, a ray, and a line segment in your notebook.

Frequent Errors and Misunderstandings

• Confusing a line segment with a line or a ray
• Measuring from the ruler’s edge rather than the zero mark
• Misnaming segments (not showing the line over the name)
• Forgetting units when writing the segment’s length

Relation to Other Concepts

The idea of a line segment is closely connected to topics like points, lines, and planes in geometry, types of angles, and polygons and triangles. Understanding line segments well will help you master area, perimeter, and even basics of coordinate geometry.

Classroom Tip

To quickly remember what a line segment is, think of a stick that starts and ends at two points. Vedantu’s teachers often use simple diagrams and ruler demonstrations during live classes for better understanding.

Quick Revision Table	Line	Line Segment	Ray
Symbol	AB (↔)	AB̅	\(\overrightarrow{AB}\)
Length	Not measurable	Measurable	Not measurable
Endpoints	No	Yes (2)	Yes (1)

Wrapping It All Up

We explored line segment—from its definition, properties, formula, examples, and connections to other concepts. Remember, practice and visual understanding make this topic simple! For more related topics, live study help, and expert-led explanations, keep learning with Vedantu.

Useful Internal Links

• Difference Between Line and Line Segment
• Ray and Line Segment
• Points, Lines, and Planes in Geometry
• Coordinate Geometry for Class 10