line segment (segment)
In mathematics, a line segment, also known as a segment, is a part of a line that consists of two endpoints and all the points between them
In mathematics, a line segment, also known as a segment, is a part of a line that consists of two endpoints and all the points between them. It can be visualized as a straight line connecting two given points.
Properties of a line segment:
1. Length: The length of a line segment can be found by measuring the distance between its endpoints. It is a positive value and can be measured in units like centimeters, inches, or meters.
2. Infinite in both directions: A line segment extends infinitely in both directions beyond its endpoints. However, the line segment itself has a finite length.
3. Straightness: A line segment is perfectly straight, meaning that it does not curve or bend at any point between its endpoints.
4. Contains all points between endpoints: All the points that lie on the line segment are called interior points. These points are enclosed within the two endpoints.
5. No points beyond endpoints: The line segment does not include any points located beyond its endpoints. These points lie outside the segment.
Notation:
A line segment can be denoted in various ways. One common notation is using the two endpoints’ letters with a line segment symbol on top. For example, if A and B are the two endpoints, the line segment would be denoted as AB or BA with a line segment symbol on top (like a horizontal bar). This notation indicates that all the points on the line segment lie between A and B.
Example:
Let’s consider a line segment AB. If point A is located at coordinates (2, 5) and point B is located at coordinates (-3, -2), we can find the length of the line segment AB.
Using the distance formula, the length of AB can be calculated as follows:
Length AB = √[(x2 – x1)^2 + (y2 – y1)^2]
= √[(-3-2)^2 + (-2-5)^2]
= √[(-5)^2 + (-7)^2]
= √[25 + 49]
= √74
≈ 8.602
Therefore, the length of line segment AB is approximately 8.602 units.
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