Collegedunia Team
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Every day, we are exposed to different shapes in our daily life, which are formed with the help of a line, or a line segment, or by drawing a curve. A line is a figure which has length but no width and a line that is enclosed between two points is known as a line segment. A ray, on the other hand, is a part of a line that has a definite starting point but no endpoint.
Read More:Integers As Exponents
Different shapes and figures can be achieved depending on the number of lines and their arrangement. A triangle, for instance, is a figure enclosed by 3 line segments, a Pentagon is a polygon defined by 5 line segments, and so on.
Table of Content
- Line Segment
- Are line segments measurable?
- Ray
- Differentiation between Line, Line Segment, and Ray
- Things to Remember
- Sample Questions
Also read: Isosceles Triangle Theorems
Line Segment
Line segments are paths that connect two points and can be measured. Polygon sides can be formed from line segments since they have defined lengths. The figure below shows a line segment known as AB, where AB's length is measured by the distance between its two ends, A and B, respectively.
Are Line Segments Measurable?
Measurement of line segments can be done with the help of a ruler (scale). As an example, let's calculate the PQ of a given segment of a line.
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- In Step 1, make sure that the tip of the ruler is placed so that the zero point is at the beginning of the given line segment.
- In step two, start reading the values shown on the ruler and locate the number which comes on the other endpoint Q.
- In Step 3, we have determined that a line segment is 4 inches long, which can be written as PQ = 4 inches.
You can denote it by using the following symbol:
A line AB segment whose ends are A and B, such as AB, is indicated with the denoted by the bar symbol (—). A line is usually denoted by the left-right arrow (↔), and a ray by an arrow (→).
Also Read:
Ray
The ray is another component of the line. There is only one terminating end and an infinitely extending end to this line segment. Its length cannot be measured because its one end is non-terminating. An arrow represents an infinitely extending part of a ray, while an endpoint represents the end of the ray.
Difference between Line, Line Segment, and Ray
Please refer to the following illustrations to understand the difference between a line, a line segment, and a ray.
| Line | Line Segment | Ray |
|---|---|---|
| A line is a set of points that extends in two opposite directions. | There are two points at the beginning and end of a line segment. | A ray is a part of a line that starts at a certain point but does not end at a certain point. |
| Arrows are shown at both ends to show that it continues indefinitely. | The length of the object is known, and its endpoints are specified. | The graph shows one start point and an arrow at the end, so it goes forever in one direction. |
| The function has no endpoints and is written as AB. | Line segment symbols are denoted by a bar on top. The symbols are written as a CD. | This is written as → EF. |
Things to Remember
- Lines cannot be measured because their ends are indefinite.
- It is possible to measure the length of a line segment since it has a start point and an endpoint.
- Each line segment has a defined length, therefore it forms the sides of any polygon.
- In the case of a ray, there is just one point of start and no point of end, so it cannot be measured.
- It is easy to understand rays using the example of the sun's rays, which have a beginning but no end.
Also Read:
Sample Questions
Ques: What are line segments?
Answer:Line segments are parts of lines that have two endpoints. In this manner, the distance between two endpoints can be measured, and a polygon can be formed.
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Ques: What is a ray?
Answer:Rays are parts of a line that have one fixed point but no definite end. Rays are defined by having one terminating end and one that extends infinitely.
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Ques: What is the difference between a line segment and a ray?
Answer:The length of a line segment can be measured because it consists of two endpoints. In contrast, a ray has only one fixed point (starting point), but no ending point. This means it cannot have a measurable length.
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Ques: How does a line segment differ from a line?
Answer:In a line, there is no endpoint and it can be extended in both directions. Line segments, on the other hand, have two endpoints and cannot be extended forward and backward.
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Ques: Is it possible to extend the line segment?
Answer:Since the line segment has two endpoints and a definite length, it cannot be extended. Alternatively, a ray can be extended in one end and a line can be extended in two opposite directions.
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Ques: What are the Steps Involved in Constructing a Line Segment?
Answer:Assuming your task is to draw a line segment of 3 centimeters. Follow the below-mentioned steps to complete your task:
- Draw a straight line of no specific measurement keeping in mind that it is longer than the line segment you have to draw.
- Mark a dot C on the line which will be the starting point of your line segment.
- Now widen the compass and using a measuring scale, ensure that the distance between the tip of the compass and the tip of the pencil is 3 centimeters apart.
- Place the tip of the compass at point C on the line that you had drawn and draw an arc 3 centimeters from point C.
- Mark the point where the arc meets the line, as D.
- Hence, CD is the required line segment of length 3 centimeters.
Read More:
CBSE X Related Questions
1.
A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin
(i) will be a 50 p coin?
(ii) will not be a ₹5 coin?
1.
A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin
(i) will be a 50 p coin?
(ii) will not be a ₹5 coin?
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2.
The table below shows the daily expenditure on food of 25 households in a locality
Daily expenditure (in Rs) 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350 Number of households 4 5 12 2 2
Find the mean daily expenditure on food by a suitable method.
2.
The table below shows the daily expenditure on food of 25 households in a locality
| Daily expenditure (in Rs) | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 |
| Number of households | 4 | 5 | 12 | 2 | 2 |
Find the mean daily expenditure on food by a suitable method.
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3.
The following table shows the ages of tha year:
Age (in years)
5 - 15
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
Number of patients
6
11
21
23
14
5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
3.
The following table shows the ages of tha year:
Age (in years) | 5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 |
|---|---|---|---|---|---|---|
Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
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4.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.
4.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.
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5.
If the median of the distribution given below is 28.5, find the values of x and y.
Class interval
Frequency
0 - 10
5
10 - 20
x
20 - 30
20
30 - 40
15
40 - 50
y
50 - 60
5
Total
60
5.
If the median of the distribution given below is 28.5, find the values of x and y.
Class interval | Frequency |
|---|---|
0 - 10 | 5 |
10 - 20 | x |
20 - 30 | 20 |
30 - 40 | 15 |
40 - 50 | y |
50 - 60 | 5 |
Total | 60 |
View Solution
6.
The following table gives the distribution of the life time of 400 neon lamps :
Life time (in hours) Number of lamps 1500 - 2000
14
2000 - 2500
56
2500 - 3000
60
3000 - 3500
86
3500 - 4000
74
4000 - 4500
62
4500 - 5000
48
Find the median life time of a lamp.
6.
The following table gives the distribution of the life time of 400 neon lamps :
| Life time (in hours) | Number of lamps |
|---|---|
1500 - 2000 | 14 |
2000 - 2500 | 56 |
2500 - 3000 | 60 |
3000 - 3500 | 86 |
3500 - 4000 | 74 |
4000 - 4500 | 62 |
4500 - 5000 | 48 |
Find the median life time of a lamp.
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