What is a line segment in math

Definition of

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The part of a line that connects two points.

It is the shortest distance between the two points.

It has a length.

Adding the word "segment" is important, because a line normally extends in both directions without end. But a line segment has definite end points.

Try moving points "A" and "B":

../geometry/images/geom-line.js?mode=seg

See: Line

A line is a straight, one-dimensional figure that extends endlessly in both directions in geometry. It has no starting and ending points. When we define a starting point but not an ending point of a line, it is called a ray. Another important term associated with the line is a line segment. What is a line segment? In the article below, we’ll learn

• The line segment definition
• Difference between line, line segment, and ray
• Line segment formula
• Line segment calculation example
• How to find the length of a line segment?
• Construction of line segment
• Understanding line segments with solved examples

Line Segment Definition Geometry

Line segment definition: A line segment is a one-dimensional figure which describes a path between two points. Unlike a line, a line segment has a definite starting point and a definite endpoint. Thus, we can measure it. Moreover, as a line segment has a defined length, it can form the sides of any polygon. 

A line segment is represented by a bar (-) on the top of its notation, say AB.

The following figure shows a line segment AB. The distance between points A and B gives the length of the line segment.  You can understand line segment geometry from the following figure.

Difference Between Line, Line Segment, and Ray

The following table states the differences between line, line segment, and ray.

Line Segment Formula

Since a line segment is a distance between two points, we can use the distance formula to calculate the length of the line segment. Thus, the line segment formula is: 

d =√(x2– x1)2+(y2 – y1)2

Line Segment Calculation Example

Example 1: What is the distance between two coordinates A (5, -13) and B (-3, 4)? Solution: We can
calculate the distance between the coordinates using the distance formula.
d = √(x2– x1)2+(y2 – y1)2
=√(-3 -5)2+(4 -(-13))2
= √(-8)2+(17)2
= √64+289
= 18.78

How to find the length of a line segment?

There are several methods to find the length of a line segment. Here we will learn three different methods.

Observation

The most trivial strategy to find the length of a line segment is to compare two line segments by simple observation. On observing, you can easily predict which one is long or short compared to the other. However, this method has several constraints, and we cannot rely completely on observation to compare two line segments.

Using Trace Paper

We can compare two line segments using the support of a tracing paper. Firstly, we will trace one line segment. Next, we will compare it with the other segment. To do this precisely, we will place the tracing paper on the other line segment. Now, notice which one is longer compared with the other. 

If we have to compare more than two line segments, then we can follow the same steps again and again. It is crucial to trace the lien segments precisely for an exact comparison of the line segments. Consequently, failure to do so puts a limitation on this procedure.

Using A Ruler

We can measure the length of a line segment with the help of a ruler (scale). Follow the steps to measure a given line segment and name it AB.

Step 1: Place the ruler along the line segment in a way that zero is placed at the starting point A of the given line segment.

Step 2: Read the values on the ruler and locate the number which comes on the other endpoint B.

Step 3: Thus, the length of the line segment is 8 inches. 

We can write it as AB = 8cm.

Construction of Line Segment

The following steps describe how to draw a line segment of 10 cm with the help of a measuring ruler or scale.

Step 1: We will draw a line of any length ( keeping the length of the line segment, i.e., 10 cm, into consideration) 

Step 2: Mark a point A on the line, which is the starting point of the line segment.

Step 3: Now, we will align a scale or ruler such that mark A coincides with 0 on the ruler.
Step 4: Locate the 10 cm on the line drawn with the help of a ruler and mark a point B. 

Step 5: Join A and B to get the required line segment of the length of 10cm.

Steps to constructing a line segment PQ of length 8 cm with the help of a ruler and compass.

Step 1: Firstly, we will draw a line of any length. This can be without any measurement, although we must consider the length of the line segment. 

Step 2: Mark a point P on the line. This will be the starting point of the line segment.

Step 3: Now place the ruler and find the pointer of the compass 8cm apart from the tip of the pencil’s lead.

Step 4: Now, place the pointer of the compass at point P on the line. Mark an arc with the same measurement using a pencil.

Step 5: Now, mark this point as point Q. So, PQ is the required line segment of length 8 cm.

Understanding Line Segment Examples with Solutions

Example 1: How would you know if the given two line segments are perpendicular to each other?

Answer: If two line segments intersect each other at 90 degrees, then the two line segments are perpendicular to each other. Also, if two lines are perpendicular, their slope is -1.

Example 2: In the following figure, mention all the line segments.

Answer: The line segments in the figure are: PQ, RS, AB, CD, MN, GH, EG, FH, NH, MG, GB, NF, ME, AM, CN, PE, RG, PF, RH, CF, CH, HD, SG, QE, MB, ND, AG, CH, FD, EB.

Example 3: Find the distance between two coordinates, A (10, -12) and B (-5, 4)? 

Solution: Using the distance formula, we can calculate the distance between the coordinates using the distance formula.

d = √(x2– x1)2+(y2 – y1)2

= √(-5-10)2+(4 -(-12))2

= √((-15)2+(16)2

= √(225+256)

=√481 = 21.93

Example 4: Name all the line segments in the following figures:

Answer: In Fig 1, there are 5 line segments. The line segments are AB, BE, DE, CD, and AC.

In Fig 2, there are 12 line segments. The line segments are AB, BC, CD, DE, EF, FG, GH, HI, IJ, JK, KL, and LA.

Example 5: How many line segments do the following shapes have:

1. Hexagon
2. Triangle
3. Pentagon
4. Circle

Answer: 1. A hexagon has six line segments.

2. A triangle has three line segments.

3. A pentagon has 5 line segments.

4. A circle has one line segment. It is known as the curved line segment. This curved line segment is the one that is creating the circle itself.

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