Measuring Line Segments: Formula, Methods & Examples

You have landed on the right page to learn about Measuring Line Segments. A line segment is a part of a line bounded by two different points in the geometry. A line segment connects two points. A line has no endpoints and can extend in both directions indefinitely, but a line segment has two defined or definite endpoints, and hence it has a finite length.

A ray differs from a line segment because a ray has just one endpoint while the other end extends indefinitely. In this article, let us explore how to find the length of a line segment, different measuring methods, and the construction of a line segment. Continue reading to know more.

Introduction

A line is a one-dimensional shape with an infinite number of points extending in any direction. A line is seen in the diagram below.

A line segment is a part or small portion of a line with two ends. \(AB\) is a line segment seen in the diagram below.

A ray is a line that starts from a single point and ends at infinity in only one direction. Look at the ray image below.

Line Segment Definition

A line segment is a part of a line bounded by two endpoints and have a finite length.

A line segment has two distinct ends. The distance between two fixed locations is the length of the line segment, which is finite and fixed. The length can be measured in metric quantities like centimetres \(\left( {{\rm{cm}}} \right)\), millimetres \(\left( {{\rm{mm}}} \right)\), and traditional measures like feet and inches.

Both endpoints are included in a closed line segment, whereas the two endpoints are not included in an open line segment. A half-open line segment is a line segment with precisely one endpoint.

Symbol

A line segment with two endpoints \(A\) and \(B\) and is denoted by the bar symbol like \(\left( {\overline {AB} } \right)\). A line is usually represented by \(\left( \overleftrightarrow{AB} \right)\) and a ray by a right arrow \(\left( {\overrightarrow {AB} } \right)\).

Line Segment Formula

A line segment can be plotted in a cartesian plane as it has a finite length. Let’s look at how to calculate the length of a line segment given the coordinates of the two endpoints. In this situation, we will utilise the distance formula, which is as follows:

\(D = \sqrt {{{\left( {{x_2} – {x_1}} \right)}^2} + {{\left( {{y_2} – {y_1}} \right)}^2}} \)

Where \(\left( {{x_1},\,{y_1}} \right)\) and \(\left( {{x_2},\,{y_2}} \right)\) are the coordinates of the given points.

Example: The coordinates of a line segment are \(\left( {1,\,2} \right)\) and \(\left( {4,\,3} \right)\) Find the distance formula to find the length of the line segment.

Here, \({x_1} = 1;\,{x_2} = 4;\,{y_1} = 2;\,{y_2} = 3\)

Substitute these values in the distance formula, we get

\(D = \sqrt {{{(4 – 1)}^2} + {{(3 – 1)}^2}} \)

\( = \sqrt {{3^2} + {2^2}} = \sqrt {9 + 4} = \sqrt {13} \) units

Hence, the length of the line segments with the coordinates \(\left( {1,\,2} \right)\) and \(\left( {4,\,3} \right)\) using the distance formula is \(\sqrt {13} \) units.

Measuring Line Segment

How do you calculate the length of a given line segment? Here, we’ll study in several ways.

1. By Observation

Simple observation is the most basic way of measuring a line segment. We can measure an unknown line segment by comparing it with another line segment of known length.

We can see that the line segment \(CD\) is longer than the line segment \(AB\) in the above diagram just by looking at it. So the measure of \(CD\) will be a bit more than that of \(AB\). However, this technique has several limitations, and we cannot always rely on observation to compare two line segments.

2. Using Trace Paper

If we have a line segment of known length and we have to find the measure of another of unknown length, we can take a tracing paper’s help. Two line segments may be readily compared with the help of tracing paper by tracing one line segment and superimposing it on the other. Repeat the method for each line segment if there are more than two.

The line segments must be traced precisely for a proper comparison. As a result, this approach is dependent on tracing accuracy, which is a drawback.

After tracing, we can approximately say the measure of the unknown line segment.

3. Using Ruler

A more accurate way of finding the measure of a line segment is by using the ruler.

As shown in the diagram below, specific marks on the ruler begin at zero and are split into equal parts. Each component is \(1\,{\rm{cm}}\) long, and these unit centimetres are further subdivided into \(10\) parts, each of which is \(1\,{\rm{mm}}\) long.

Place the zero marking of the ruler near the beginning of the line and measure its length accordingly to measure a line segment \(AB\).

In the figure given above, the length of line segment \(AB\) is \(6.7\,{\rm{cm}}\). But there can be errors. We might have difficulty reading over the marks in the pointer. We can also have positioning errors.

If our eyes are not vertically on top of the object, we may get errors due to angular viewing. How do we get rid of such errors? That is done with the help of a divider.

4. Using Ruler and Divider

A divider is used to correct the positioning error. Place one of the divider’s needles at \(A\) and the other at \(B\), align the divider with the ruler and measure its length. This approach is more precise and reliable.

Suppose we want to measure the length of line segment \(AB\).

We follow the following steps:

1. First, we take a ruler and put its two tips of legs at the endpoints of the line.

2. Without changing the divider’s position, place it near the ruler, with its one leg tip at the zero marking of the ruler.
3. Then use the ruler to measure the distance between the two endpoints of the divider.

Measurement using a ruler and divider gives the most accurate and precise measurement of any line segment.

Construction of Line Segment

The most straightforward way for drawing a line segment of the appropriate length is to use a ruler.

1. Take a scale and look for the zero marking, which is the beginning of the scale.
2. Place the scale on the piece of paper and use a dot to mark the beginning of the line segment. Mark it with a point \(A\).
3. Mark the line segment’s endpoint, i.e. till it reaches the desired length, say \(8\,{\rm{cm}}\). Put a \(B\) next to it.
4. Connect the two locations with a straight line. We’ll obtain a \(8\,{\rm{cm}}\) long line segment \(AB\).

Solved examples– Measuring Line Segments

Q.1. Identify if the given figure is a line segment, a line, or a ray.

Ans: The figure has one starting point but an arrow on the other end which shows that it is not a line segment or a line but a ray. Therefore, \(PQ\) is a ray.

Q.2. Draw a line segment of a given length \(6\,{\rm{cm}}\).
Ans: The steps to draw a line segment are as follows:
1. Take a scale and look for the zero marking, which is the beginning of the scale.
2. Place the scale on the piece of paper and use a dot to mark the beginning of the line segment. Mark it with a point \(A\).
3. Mark the line segment’s endpoint, i.e. till it reaches the desired length, say \(6\,{\rm{cm}}\). Put a \(B\) next to it.
4. Connect the two locations with a straight line. We’ll obtain a \(6\,{\rm{cm}}\) long line segment \(AB\).

\(AB\) is the required line segment.

Q.3.  Draw any line segment, say \(AB\). Take any point \(C\) lying in between \(A\) and \(B\). Measure the lengths of \(AB,\,BC\) and \(AC\). Is \(AB = AC + CB\)?
Ans: Let \(AB\) be a \(6\,{\rm{cm}}\) long line segment with point \(C\) located between \(A\) and \(B\).

When it comes to determining the lengths of line segments,
Using a ruler, we observe that \(AB = 6\;{\rm{cm}},\,AC = 3.5\;{\rm{cm}}\), and \(CB = 2.5\;{\rm{cm}}.\)
Now that \(AC + CB = 3.5 + 2.5 = 6\;{\rm{cm}} = AB\)
Hence, \(AC + CB = AB\)

Q.4. What is the disadvantage in comparing line segments by mere observation?
Ans: There’s a risk you’ll make a mistake because you’re looking at it incorrectly. When two line segments of almost equal length are compared, we cannot determine which line segment is longer. We can’t compare line segments with minor length differences just by looking at them. Hence, there are more chances of errors due to improper viewing.

Q.5. Why is it better to use a divider than a ruler while measuring the length of a line segment?
Ans: When measuring the length of a line segment, it is preferable to use a divider rather than a ruler since the divider will produce a more precise result, but the ruler may not. A positioning mistake in a ruler is possible.

Summary

In this article, we have discussed the definition of a line, line segment and a ray. After that, we discussed different methods to measure a line segment, such as by observation, tracing paper, and using a ruler and a compass. Also, we sew the formula to find the length of a line segment and steps to construct a line segment.

Frequently Asked Questions

Q.1. Which device do you use to measure a line segment?
Ans: We use a ruler to measure a line segment.

Q.2. What is the symbol for the line segment?
Ans: A line segment with two endpoints \(A\) and \(B\) and is denoted by the bar symbol like \(\left( {\overline {AB} } \right).\) A line is usually represented by \(\left( \overleftrightarrow{AB} \right)\) and a ray by a right arrow \(\left( {\overrightarrow {AB} } \right)\).

Q.3. How do you draw and measure a line segment?
Ans: The most straightforward way for drawing a line segment of the appropriate length is to use a ruler.
1. Take a scale and look for the zero marking, which is the beginning of the scale.
2. Place the scale on the piece of paper and use a dot to mark the beginning of the line segment. Mark it with a point \(A\).
3. Mark the line segment’s endpoint, i.e. till it reaches the desired length, say \(5\,{\rm{cm}}\). Put a \(B\) next to it.
4. Connect the two locations with a straight line. We’ll obtain a \(5\,{\rm{cm}}\) long line segment \(AB\).

Q.4. How do you measure a line segment with a ruler?
Ans: Place the zero marking of the ruler at the beginning of the line. Align the ruler along the line and measure its length till the other endpoint on the ruler.

Q.5. Which are the examples of a line segment?
Ans:  A pencil, a baseball bat, the cord to your cell phone charger etc., are some of the examples of a line segment.

We hope this detailed article on the concept of measuring line segments helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!