A line segment is a finite section of a straight line with two endpoints and a fixed length. In contrast, a line extends infinitely in both directions without specific endpoints. This article explores the definition, properties, formulas, and terminology of line segments, along with methods for measurement. It includes solved examples and practice questions for a better understanding of the concept of this article.
What is Line Segment?
A line segment is a straight path between two points in space.
It is the shortest distance between those two points and is characterized by having a definite length and direction. Unlike a line, which extends infinitely in both directions, a line segment has a fixed beginning and end point.
Real-life examples of Line Segment
Real-life examples of Line Segments are the edges of a table, a pencil, matchstick, edges of scale, edges of paper, sides of polygon etc. Under geometrical shape, a triangle consists of three Line Segments, and in the case of quadrilateral, it has four Line Segments.
Representation of Line Segment
Let’s suppose a Line Segment with two endpoints C and D whose length is fixed. The length of this Line Segment is measured by the distance between a point C and D. It is represented by a bar (-) on top of CD. It is written as CD with a horizontal line on top of C̅D̅.
Properties of Line Segment
The properties of Line segments are listed below:
- A Line Segment is not an infinite endless line but a section of a line with two distinct endpoints.
- A Line Segment has two fixed or definite endpoints.
- The length of a Line Segment is measured by shortest distance between these fixed points.
- A Line Segment is symbolically represented by a bar ‘―’ on the top of two points or C̅D̅ .
Types of Line Segment
Based on the properties of line segments, they are classified into various types. Some of them are listed below:
- Congruent Line Segments
- Parallel Line Segments
- Intersecting Line Segments
- Perpendicular Line Segments
Congruent Line Segments
Two line Segments are said to be congruent if the they are equal in length. For Example, the sides of a square are congruent line segments.
Parallel Line Segments
Two line segments are said to be parallel if the distance between them at every point is same. The opposite sides of a rectangle or a parallelogram are parallel line segments.
Intersecting Line Segments
Two line segments are said to be intersecting line segments if they meet at a common point. For Example, the adjacent sides of a rectangle and parallelogram are intersecting lines.
Perpendicular Line Segments
If two line segments intersect each other at 90° then they are said to be perpendicular line segments. For Example, the adjacent sides of square or rectangles are perpendicular segments.
Line Segment is a part of the line that can link two fixed or definite endpoints. Lets suppose the coordinates of starting point “C” and an end point “D” on a given Line segment is (x1,y1) and (x2,y2). Now we can calculate the length of Line segment by using distance formula.
D = √(x2 - x1)2 + (y2 - y1)2
How to Find the Midpoint of a Line Segment?
To find the midpoint of a line segment, we have two different methods. These methods are:
- Counting Method
- Using the midpoint formula of a line segment
Counting Method
To find out the midpoint, measure the length of the given Line segment and then move half of that length and calculate the value from either of the two endpoints. For a vertical line segment, move vertically from the bottom or top endpoint, and for a horizontal line segment, move horizontally from the leftmost or rightmost endpoint. The point where you get the required length is called midpoint of the Line segment.
Midpoint Formula Method
By using the Midpoint Formula Method, we can find out the midpoint of given line segment that exists diagonally across the coordinate axis. The midpoint (x,y) of the line segments with the coordinates of two endpoint C (x1, y1) and D(x2, y2) can be calculated by using the midpoint formula.
Midpoint (x, y) = [(x1 + x2)/2, (y1 + y2)/2)]
Difference Between Line, Line Segment, and Ray
Line, Line Segment and Rays are fundamental for geometrical figure. They sound and look similar but have significant difference between them.
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Let's learn the difference between Line, Line segment and Rays in tabular form:
Line
| Line Segment
| Ray
|
|---|
A Line is a collection of points that go forever in two opposite directions indefinitely. It is an endless continuous and it has no finite endpoints
| Line Segment is a part of the line that can link two fixed or definite endpoints, in which all points exist between these end points.
| When a line has a starting point but not a finite end point means end at infinity is called a Ray.
|
It is represented with arrows at both ends to show that it extends infinitely in both directions.
| It has a definite length and it does not extend infinitely in both the direction.
| It represents one start point and an arrow at the other end that means it moves forever in one direction.
|
It is represented by ↔.
| It is represented by a bar ‘―’ on the top of two endpoints.
| It is represented by →.
|
Line Segment Measurement
There are various methods to measure the length of a Line Segment. Here we will discuss the three different methods.
Observation Method
In this method, the length of Line segment is measured by comparing the two Line segments by simple observation. This method is easily predicable method that which one is longer or shorter compared with others. However, this method does not give the exact measurements by observation and comparisons; we cannot rely completely on this method to compare two Line Segments.
Trace Paper Method
In this method, the length of Line Segment is easily measured by comparing the two line segments with the support of a tracing paper.
Step 1: Firstly, we will trace one Line segment and compare it with other segment.
Step 2: Next, we will put carefully the tracing paper over the other Line segment.
Step 3: Now, we will observe which one is longer than the other.
Step 4: In case of multiple Line segments, we will repeat this process again and again.
How to Draw a Line Segment?
We can draw a Line Segment using two methods, first by scale and second by Compass and Ruler. Let's learn the steps of these methods
Construction Line Segment using Ruler
With the help of Scale (Ruler), we can measure a Line segments. Let us suppose a line segment between two endpoints and name it CD.
Step 1: Take a centimeter scale to measure the length of Line segment. Put the tip of the scale at i.e. zero centimeter carefully on the starting point C of the given line segment.
Step 2: Now, start read the value given on the scale and stop at the number or value which comes on the endpoint D.
Step 3: Thus, in this case for example the length of the given Line segment is 6cm, which can be written as C̅D̅ = 6cm.
Construction of Line Segment using Compass
With the help of Ruler and Compass, we can measure a Line segments. The steps for constructing the line segments are:
Step 1; Firstly, we will draw a line of any length without any measurement.
Step 2: Mark a starting point C on the line.
Step 3: After that, take a ruler and put the pointer of compass at the initial point of ruler as zero and expend the tip of pencil lead to the output point of ruler i.e. the required length of Line segment. Here we say it 6cm.
Step 4: Now, mark output point as point D. So, CD is the required length of Line segment 6cm.
Also, Check
Solved Problems on Line Segment
Example 1: Find the distance of the Line Segment CD if the coordinates of C and D are (3, 5) and (2, 1) respectively.
Solution:
Given coordinates of Line Segment CD is (3, 5) and (2, 1).
x1=3, y1=5, x2=2, y2=1.
Apply the distance formula:
D = √(x2-x1)2 + (y2-y1)2
= √(2-3)2 + (1-5)2
=√1+16
=√17
= 4.12unit
Therefore, the length of Line Segment CD is 4.12unit.
Example 2: Find the length between two coordinates, C (9, -12) and D (-4, 4) of Line Segment CD?
Solution:
Given coordinates of Line Segment CD is (9,-12) and (-4,4).
x1=9, y1= -12, x2= -4, y2=4.
Apply the distance formula:
D = √(x2-x1)2 + (y2-y1)2
= √(-4-9)2+(4 -(-12))2
= √(-13)2+(16)2
= √225+256
=√481 = 21.93unit
Therefore, the length of Line Segment CD is 21.93unit.
Example 3: A length of Line Segment is 8 cm. If the ratio of the lengths of one part to the other part is 3:4, find the lengths of these two parts.
Solution:
Suppose the lengths of the two parts are 3x and 4x
As per the given ratio, we have 3x:4x=3:4
After cross-multiplying, we get 4(3x)=3(4x)
After simplifying,
12x=12x
Here, sides are equal, we put any value of x, and it will satisfy the equation. Put the value of x=1.
Therefore, the lengths of the two parts are 3x=3(1) = 3cm and 4x=4(1) = 4cm.
Example 4: Find the length of Line Segment CE, if the length of CD is 22unit. In a Line segment CD, the ratio of the length of CD to the length of CE is 6:3
Solution:
Suppose the length of CE be x units.
As per the given ratio, we have CD:CE=6:3
Put the values, we have 22:x=6:3
After cross-multiplying, we get 6x=3×22
After simplifying, 6x=66
x=11
Therefore, the length of CE is 8units.
Practice Questions on Line Segment
Q1. By using a ruler or scale, draw a Line Segment of 6 cm.
Q2. By using a ruler and compass, draw a Line Segment of 6.5 cm.
Q3. How many Line Segments do the following shapes have: hexagon, triangle, and pentagon?
Q4. Write the definition of Line, Line Segment and Ray.
Q5. Find the distance of the Line Segment CD if the coordinates of C and D are (7, 5) and (3, 1) respectively.
Q6. A length of Line Segment is 10cm. If the ratio of the lengths of one part to the other part is 7:3, find the lengths of these two parts.
Q7. Find the length of Line Segment CE, if the length of CD is 40unit. In a Line segment CD, the ratio of the length of CD to the length of CE is 11:7.
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