Line Segments

In this article, we want to introduce you to the line, line segment, ray, features of each, and their differences.

Line Segments

Line segments are paths in-between \(2\) points that you can measure. Because line segments have defined lengths, they can create the sides of polygons. It’s not the same as a line that doesn’t have any beginning or end and that can be expanded in \(2\) directions.

Line segments are represented by a bar on top, that’s the symbol for line segments.

Related Topics

Way to Measure a Line Segment?

A line segment can be measured via the assistance of a ruler (scale). Here’s the way to measure a particular line segment and call it \(PQ\).

  • Step one: Put the ruler’s tip carefully at the Zero so it is put at the beginning point \(P\) of the particular line segment.
  • Step two: Then, begin to read the values provided on the ruler and see which number comes on the additional endpoint \(Q\).
  • Step three: So, the line segment’s length equals four inches, which you can write as \(PQ¯\) \(=\) four inches.


The formula for a Line Segment

In the example above, we calculated the line segment’s length as \(PQ\) to be four inches. That is put down as \(PQ¯ = 4\) inches. So, let’s find out the way to locate a line segment’s length whenever the coordinates of the \(2\) endpoints are provided. In this instance, we utilize the distance formula, which is, D = \(\sqrt{(x2-x1)^2+ (y2-y1)^2}\). Then, \((x1, y1)\) and \((x2, y2)\) are coordinates of the particular points.

LineLine SegmentRay
A line is a set of points that extend in \(2\) opposite directions forever.A line segment is a part of a line with a starting point and an endpoint.A ray is a part of a line with a starting point yet no obvious endpoint.
It is shown with arrows at both ends to signify it goes on forever.It has a distinct length and is shown with \(2\) endpoints.It shows one starting point and an arrow at the other end which means it continues forever in a single direction.
It hasn’t any endpoints and is written as ←→ABAB↔.It is signified by a bar on top which is the line segment symbol. It is written as ¯CDCD¯.It is written as −→EFEF→

Line Segments – Example 1:

Determine whether the following shape is a line, a line segment, or a ray.

Solution:

This shape is a line segment because it is a part of a line with a starting point and an endpoint.

Line Segments – Example 2:

Determine whether the following shape is a line, a line segment, or a ray.

Solution:

This shape is a line because it is shown with arrows at both ends to signify it goes on forever.

Exercises for Line Segments

Determine whether the following shapes are a line, a line segment, or a ray.

1)

2)

This image has an empty alt attribute; its file name is answers.png
  1. ray
  2. line segment

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Math and Critical Thinking Challenges: For the Middle and High School Student