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# Line Segment|Definition & Meaning

## Definition

In **geometry,** a line **segment** is seized by two **characteristic pinpoints** on a line. Or we can also say that a **line** segment is a piece of the **line** that joins **two** points.

A **line** segment has two **factual** points in a line. The **distance** of the line **segment** is set, which is known as the **length** between two allotted **points.** The distance here can be calculated by metrical units such as **centimeters** (cm), and **millimeters** (mm) or also by traditional units like feet or **inches. **

## Ray, Line, and Line Segment

A line has no **terminal** points and **lengthens** without limit in both paths while a line segment has two set or precise endpoints. The discrepancy between a Line **segment** and a ray is that a ray has only one terminal point and the other end of the ray grows infinitely or without any **measure.**

A one-dimensional form and cluster of points **expanding immeasurably** in both directions is known as a line. A portion of a line that has two endpoints or terminal points and there is a brief **distance between** them, is named a** line segment**. A ray starts at one terminal point and finishes at infinity. Figure 1 depicts the image of the **ray, line,** and line **segment.**

### Important Notes

A **line** has **undefined** ends and **therefore** it cannot be **estimated** whereas, a line **segment** has a beginning point and an ending point, thus, it can be **measured.** Line **segments** have a **specified** length, consequently, they **create** the margins of any **polygon.** A ray has just one **start** point and no **ending** point, accordingly, it **cannot** be **calculated.**

The idea of rays can be **comprehended** with the **sample** of the rays of the sun, **which** have a start point but no **stopping** point.

## Line Segment Definition

A **line segment** has two concrete **stopping** points in a line. The **distance** of the line segment is **predetermined,** which is the length **between** two set points. The **distance** here can be gauged by **metrical** units such as **centimeters** (cm), and **millimeters** (mm), or also by traditional units namely **feet or inches**.

A **bounded** line segment comprises both **ending** points, while an open line **segment** is the sole of the two **ending** points. A line **segment** that has exactly only one **ending** point is **named** a **half-open** line **segment.**

A **line** segment with two ending points, we say as **A** and **B**, is denoted by the bar **character (—)** such as $\overline{AB}$.

## Measuring Line Segment

Given **below** are the methods we can use to **calculate** the Line **segment.**

### By Observation

The **easiest** method of **comparing** the two line segments is **simple** **observation**. Just by watching these **two** line segments, one can **easily** foretell which is lengthy or tiny in **contrast** to the other.

In the **above** image, by **observing** it, we can say that **line segment** **AB** is more in the **distance** as corresponded to line segment **CD**. But this **methodology** has various **limitations, every** time we cannot **depend** entirely on **observation** to **differentiate** between two line **segments.**

### Using Trace Paper

With the **aid** of trace paper, two line **segments** can be **effortlessly** juxtaposed. For this, **firstly,** trace one line segment and put it over on the **second segment** which is to be compared, and it can be **readily concluded** which is more significant in length. For more **additional** line **segments,** reprise the **process** repeatedly.

For **accurate differentiation,** the line segments must be **outlined precisely.** Therefore this **procedure** relies on the precision of **outlining,** which sets a constraint on this **process.**

### Using Ruler and Divider

There are **characteristic** marks on the ruler starting from 0, as shown in the figure provided below. These **arrangements** separate the **ruler** into similar pieces. Each **portion** is similar to a **distance** of one cm, and these unit **centimeters** are also sectioned into ten portions, and each part is equal to one **millimeter.**

To **calculate** a line segment **AB,** put the 0 mark of the **ruler** on the edge of the **start** of the line and **gauge** its distance **consequently.**

In the **picture** given above, the distance of line segment **AB** is **3** cm.

To **eradicate** the location error we **utilize** a divider. **Establish** one needle of the **divider** at point A and the other at **point B** and then put the **divider** on the ruler and **calculate** its length. This **approach** is better **authentic** and **unfailing.**

## Line Segment Formula

As we **understand,** a line segment has **two** ending points. Now if we **comprehend** the **counterparts** of the ending points, then we can also compute the **distance** of the line segment by the **distance** formula:

\[ D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\]

**Consider** a line **segment** with the correlates** (4, 2)** and **(–3, –4)**. Its line **segment** can be **discovered** as:

**Consequently,** by distance **formula:**

\[ D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\]

\[ D = \sqrt{(-3-4)^2 + (-4-2)^2 }\]

\[ D = \sqrt{(-7)^2 + (-6)^2 }\]

\[ D = \sqrt{49 + 36}\]

\[ D = \sqrt{85}\]

\[ D = 9.219\]

## Construction of Line Segment

Here we will **understand** to sketch a line **segment** with the aid of a **compass** and measuring scale or ruler. Let us **presume,** we **require** to sketch a line **segment** of a distance of 7cm. Then pursue the **beneath-given** steps:

**Sketch**a line of any length without**measuring**it (keeping in attention the**distance**of the line segment)- Draw a point
**A**on the line, the**beginning**point of the line segment. - Now
**utilizing**a scale, discover the**arrow**of the compass 7cm apart from the**pencil’s**tip. **Likewise,**place the arrow of the compass at**point P**on the line, and with the**exact**measure draw an arc with the pencil.- Now, call this
**point****B**

**Thus,** AB is the demanded line **segment** of length **seven** cm.

## Examples of Line Segments

**Mostly** the dominant **samples** are noticed in** 2D** geometry, where per polygon is **assembled** by a sequence of **line** segments.

- A
**hexagon**is created of**6 line**segments united end to end - A
**rectangle**is created of**4 lin**e segments - A
**pentagon**is constructed of**5 line**segments

Thus, line segments achieve an essential role in geometry.

## Line Segment: Solved Examples

### Example 1

A **line segment** is provided by the **endpoints** (4, 2) and (10, –6). Measure its length.

### Solution

**Utilizing** the distance formula for the **procedure:**

\[ D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\]

\[ D = \sqrt{(10-4)^2 + (-6-2)^2 }\]

\[ D = \sqrt{(6)^2 + (-8)^2 }\]

\[ D = \sqrt{36 + 64}\]

\[ D = \sqrt{100}\]

\[ D = 10\]

*All images/mathematical drawings were created with GeoGebra.*