Drawing Lines: A line is a straight one-dimensional figure made of infinitely many points, having no thickness and extending infinitely in both directions. A line segment is a section of a line with two endpoints. It is one of the most important aspects of practical geometry since it aids in creating geometric forms and figures. \(AB\) denotes a line segment having two ends, \(A\) and \(B.\)

However, how do you make a line segment? Do we draw a line segment using the same tool that we use to measure it? In this article, we will discuss how to draw different lines.

Line and Line Segment

A line is a set of infinite points that extends indefinitely on both sides of a plane. Horizontal, vertical, diagonal, oblique, or curved lines are all possibilities. Two lines can be perpendicular or parallel. It doesn’t matter if the lines are thick or thin. Curved lines change direction as well.

A line segment is a set of finite points with a predetermined length. It has a beginning and a conclusion. It is the smallest measurable distance between two locations. We can use a ruler or an inch scale to determine its length. A line segment is a section that makes up a line. A line segment \(AB\) is shown below.

Learn All the Concepts on Lines

Line segments form any two-dimensional shape. A few polygons are shown here. Three-line segments create a triangle, five-line segments make up a pentagon, and four-line segments make up quadrilaterals. The number of sides a polygon has determined its name. Line segments form the sides.

Types of Line

1. Straight Line: A straight line is the collection of infinitely many points extending in either direction endlessly.

2. Curved Line: A curved line is not straight but instead, have bends.

3. Parallel lines: Parallel lines are two lines on a flat surface that do not intersect at a point. Parallel lines are those that do not cross or intersect at a point. It is symbolized by the symbol \(||.\)

4. Intersecting Lines: Lines that intersect at the same place are called intersecting lines. The point of intersection is the name given to this common location.

5. Perpendicular Lines: When two lines cross so that the angles produced between them are right angles, they are said to be perpendicular.

6. Ray: Ray is a collection of points that may be stretched in one direction indefinitely. A ray is a part of a line with one end or origin and continues endlessly in the opposite direction.

Let’s look at an illustration to understand the topic better. Take a look at the \(\overrightarrow {AB} \) ray below.

\(P\) is the endpoint of the ray \(\overrightarrow {PQ} ,\) which can be extended indefinitely in the direction of point \(B.\)

Methods to Draw a Line Segment

A line segment is a section of a line that has a start and an endpoint. It has a certain length and is identified by the line segment sign, a bar on top like \(\overline {AB} .\) We may use any of the following ways to create a line segment of a specific length:
1. Using a ruler to draw a line segment
2. Using a ruler and compasses to draw a line segment

Drawing a Line Segment Using Ruler

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

Step 1: Take a scale and look for zero as the starting point.
Step 2: Place the scale on the piece of paper and use a dot to mark the beginning of the line segment. Mark it with an \(A.\)
Step 3: Mark the line segment’s terminus, i.e., till it reaches the desired length, say \(6\,{\text{cm}}.\) Put a \(B\) next to it.
Step 4: Connect the two locations with a straight line. We’ll obtain a \(6\,{\text{cm}}\) long line segment \(AB.\)

If we extend this line segment \(\overline {AB} .\) in either direction, we will get the line \(\overleftrightarrow {AB}.\)

Drawing a Line Segment Using Ruler and Compass

Using a ruler and compasses is another way to draw a line segment. This is a more precise approach, but it needs more attention.

Step 1: Draw a line of any length in the first step.
Step 2: Mark a point and make point \(A\) the starting point of the line segment.
Step 3: Take a ruler and set the compass pointer at \(0\) markings of the ruler, then open the compass to reach the pencil tip at a distance of \(6\,{\text{cm}}{\text{.}}\)

Step 4: Keeping the compass pointer at \(A,\) draw an arc with the pencil tip without altering the length. Mark the meeting point as \(B\)
Step 5: Draw a line from the junction of the arc and the line to point \(A.\)

Step 6: The needed line segment is \(AB,\) which is \(6\,{\text{cm}}\) long.

Steps to Draw Perpendicular and Parallel Lines

When drawing parallel lines, keep in mind that the spacing between the lines must always be the same. Using a protractor and a ruler, create perpendicular and parallel lines, as shown below. We would want to draw a line parallel to \(XY\) that passes through point \(A.\)

Step 1: Draw a line perpendicular to \(A\) and \(XY.\) Draw a line through \(A\) that is \({90^ \circ }\) degrees to \(XY\) using your protractor. The point \(C\) where your new line meets \(XY\) should be labelled. If you get stuck, look at the diagram below.

Step 2: Find the distance between the point \(A\) and the line that is perpendicular to it. Make a note of the length of \(AC.\)
Step 3: Draw a point on the line some distance away. Draw a perpendicular line to line \(XY\) and mark off the same length as \(AC\) on that line. The drawing illustrates what you must do.

Step 4: Make a parallel line. Connect \(A\) to a new point that is an equal distance from \(XY.\) A parallel line has now been created.

Solved Examples – Drawing Lines

Q.1. M and N are points on the blue and purple lines, respectively. If the distance between M and the purple line is \(6\,{\text{units}}.\)

What is the shortest path between N and the blue line?
Ans: Because the lines are parallel, they are all equidistant.
This indicates that the perpendicular distance between \(M\) and the purple line is the same as the distance between \(N\) and the blue line. As a result, this distance is \(6\,{\text{units}}.\)
The perpendicular distance between the two lines is the smallest distance between them. The shortest distance between \(N\) and the blue line is thus \(6\,{\text{units}}.\)

Q.2. A square is made up of how many line segments?
Ans: A square is made up of four-line segments. A vertex or corner is the place where two-line segments meet. As a result, a square has four sides and four corners.

Q.3. Write down the two differences between a line, a line segment, and a ray.
Ans:

Line	Line segment	Ray
A line is a length that has no width.	A line segment is a fixed-length section of a line.	A ray is a segment of a line that begins at one point and extends in a single direction.
The line has no finite length endpoints.	The line segment has two fixed endpoints.	There is only one endpoint to a ray.

Q.4. Classify each of the following into lines and line segments.

Ans: We can easily classify them since we know that a line stretches indefinitely and that a line segment has endpoints. Thus,
Line: \(AB\)
Line Segments: \(ST,XY,\) and \(XY,YZ,XZ\) (sides of triangle \(XYZ\))

Q.5. Recognize and label the line segments.

Ans: A line segment has two endpoints, as we all know. Naming the line segments by their endpoints is simple. Thus,
a) \(AB\) and \(CD\)
b) \(PQ,PR,RQ,\) and \(RS\)
c) \(DE\) and \(EF\)

Summary

A line is a set of infinite points that extends indefinitely on both sides of a plane. A line segment is a section of a line that has a start and an endpoint. One can create a line segment by using a ruler. One can also draw a line segment of a specific length by using a ruler and compass. One can also identify the line and line segment, ray and differentiate between the line, line segment, and ray by using several techniques.

Learn About Parallel and Perpendicular Lines

Frequently Asked Questions (FAQs)

Q.1. How do you find the length of a line segment?
Ans: The distance between the two ends of a line segment can be used to determine its length.

Q.2. What are the tools used to construct the parallel and perpendicular lines?
Ans: We use a ruler, a compass, a protractor, etc., to construct the parallel and perpendicular lines.

Q.3. How do you determine the perpendicular lines?
Ans: The perpendicular lines are formed when the angle between the lines is \({90^ \circ }.\)

Q.4. How do you construct the perpendicular line?
Ans: 1. Draw a line and find any point that isn’t on it.
2. From where the provided line crosses the supplied line at two spots, draw an arc of any radius.
3. Draw two circles from two places on the line segment.
4. Connect the location to the points where two circles overlap.

Q.5. How do you identify the parallel lines?
Ans: The lines that do not intersect and are of the same length.

Now you are provided with all the necessary information on drawing lines and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.