The Essential Guide to Line Segments: Properties, Naming, and Length Calculation

Line Segment

A line segment is a straight line that connects two points

A line segment is a straight line that connects two points. It is a part of a line that has a fixed length and has two distinct endpoints. The length of a line segment can be measured by finding the distance between the two endpoints using various methods.

Naming a Line Segment:
A line segment is often named using its endpoints. For instance, if a line segment connects point A and point B, it can be denoted as AB.

Length of a Line Segment:
To find the length of a line segment, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula states that the distance (d) between two points (x1, y1) and (x2, y2) in a coordinate plane can be calculated using the following equation:

d = √((x2 – x1)^2 + (y2 – y1)^2)

For example, consider a line segment with endpoints A(3, 4) and B(7, 9). The distance between these two points can be found as follows:

d = √((7 – 3)^2 + (9 – 4)^2)
= √(4^2 + 5^2)
= √(16 + 25)
= √41

Therefore, the length of the line segment AB is √41 units.

Properties of Line Segments:
Here are some important properties of line segments:

1. Length: A line segment has a specific length, which can be measured in units such as inches, centimeters, or meters.

2. Midpoint: The midpoint of a line segment is the point that divides the line segment into two equal halves. It is equidistant from both endpoints. The coordinates of the midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.

3. Collinearity: Any three points that lie on a line segment are said to be collinear. In other words, if points A, B, and C are on the same line segment, then they are collinear.

4. Addition Property: The length of a line segment can be added to the length of another line segment if they share an endpoint. For example, if AB is a line segment of length 5 units and BC is a line segment of length 3 units, then the length of AC would be 8 units.

These are some essential concepts related to line segments. Understanding these properties and the formula for calculating length will help you solve problems involving line segments in math.

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