What is a Line?
The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A line is a collection of points forming a one-dimensional shape and extending infinitely in either direction. The figure below depicts a line:
What is a Ray?
A ray has one start point and an end point of infinity. The illustration provided describes a ray.
What is a Line Segment?
When we consider a line segment, it has two distinct endpoints. The length of the line, which is the separation of two fixed points, is constant. The length can be calculated in feet or inches, or in metric units like centimeters (cm) or millimeters (mm). In contrast to an open line segment, which excludes the two endpoints, a closed line segment includes both endpoints. A half-open line segment is a line segment with one endpoint.
Hence, we now know that a line segment is the portion of a line that connects two end points and is the shortest path between them.
Symbol
The bar symbol (—) is used to represent a line segment with the end points A and B : \(\overline{AB}\)
A line is usually represented by (\(\leftrightarrow\)) and a ray by a right arrow (\(\rightarrow\)).
Measuring a Line Segment
Here, we will learn about a variety of techniques to measure a line segment.
Using observation
Simple observation is the simplest way to compare two line segments. One can tell which of two line segments is longer or shorter simply by looking at them.
By Using Tracing Paper
Two line segments can be easily compared using tracing paper. It is simple to determine which line segment is longer by tracing one of them and placing it on top of the other. Repeat the process several times to cover more than two line segments.
Accurate tracing of the line segments is necessary for a precise comparison. As a result, this method is constrained by its dependence on the accuracy of tracing.
Using a Divider and a Ruler
As can be seen in the image, a ruler has some markings that start at zero and divide it into equal portions. These unit centimeters are further divided into 10 parts, each of which is equal to 1 millimeter in length. Each part is equal to a length of 1 centimeter.
A divider on the other hand looks like a compass but it has two sharp ends instead of a pencil on one end. Measuring the distance between two endpoints of a line segment with a divider involves placing one sharp end of the divider on one point and extending the other arm of the divider till the second sharp end aligns perfectly with the second point of the line segment. Place the extended divider, with one of the ends placed on the zero mark of a ruler. Observing the mark where the second arm of the divider points to, provides the length of the line. Using this method the lengths of different line segments can be measured and compared.
Construction of a Line Segment
Here, we’ll cover how to use a compass and measuring ruler or scale to draw a segment of a line.
Let’s say we need to draw a 7 cm long line segment. then adhere to the instructions below:
- Draw a line without measuring its length (keeping in consideration of the length of the line segment).
- The line segment will begin at point A, which you should mark on the line.
- Now, place the compass pointer 7 cm away from the pencil using a scale or ruler.
- Place the pointer of the compass at point A once more on the line, and using the same measurement, draw an arc with the pencil.
- Mark this point as B now.
Therefore, AB is the 7 cm long line segment that is needed.
Line segment Examples
The most prevalent examples can be seen in 2D geometry, where every polygon is made up of individual line segments.
- Three end-to-end line segments are joined to form a triangle.
- Four-line segments form a square.
- Five-line segments form a pentagon.
So this shows that line segments are crucial in geometry.
Solved Examples
Based on the diagram, answer the following questions:
Example 1: Write the name of any one ray.
Solution:
There are two rays present in the given figure: UT and PQ (with arrows in one direction)
Example 2: Write the names of two line segments in the figure.
Solution: Two line segments are:
Line segment 1: UQ (without arrow part)
Line segment 2: PR (without arrow part)
Example 3: Direct ferry routes are available between each pair of cities on the map given in the image. Draw the line segments to represent all of the possible ferry routes and find the possible number of ferry routes between them.
Solution:
Start at Jersey. Draw a line segment from Jersey to each of the other cities. We will repeat this process until a route is shown between each city.
So, we find that there are 3 ferry routes between the given cities as shown in the figure.
In comparison to a line that extends indefinitely on both ends, a line segment has two endpoints.
A line segment has two endpoints while a ray only has one. While the endpoints of a line segment are always definite, one end of a ray can extend indefinitely.
The line segment can be a stick, a scale, a ruler, a boundary line, etc.
An element of a line is a line segment. It has two endpoints on either side to signify the beginning and end of the line segment, respectively. A line segment is any side of a shape and not a shape by itself. For instance, squares have four line segments while triangles have three.
A point is a distinct, exact location that can be described by a single pair of coordinates on a graph. Between two points, a segment exists. A ray has a single point of origin and travels in one direction indefinitely. An endless line extends in both directions.