Calculating the Length of a Line Segment

Oct 13, 2025 by wbrum.org 136 views

Introduction

In geometry, a line segment is a part of a line that is bounded by two distinct points. Finding the length of a line segment is an essential concept in mathematics, and it has numerous applications in various fields such as physics, engineering, and computer science. In this article, we will discuss how to find the length of a line segment given its endpoints.

What is a Line Segment?

A line segment is a part of a line that is bounded by two distinct points. It is a straight line that connects two points and has a definite length. The two endpoints of a line segment are called the vertices or endpoints of the line segment.

Calculating the Length of a Line Segment

To find the length of a line segment, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.

Example: Finding the Length of a Line Segment

Let's consider an example to illustrate how to find the length of a line segment. Suppose we have two points (7, 2) and (-2, 2). We want to find the length of the line segment that connects these two points.

Step 1: Identify the Endpoints

The two endpoints of the line segment are (7, 2) and (-2, 2).

Step 2: Apply the Distance Formula

To find the length of the line segment, we will apply the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (7, 2) and (x2, y2) = (-2, 2).

Step 3: Calculate the Distance

Substituting the values into the distance formula, we get:

d = √((-2 - 7)² + (2 - 2)²) d = √((-9)² + 0) d = √(81 + 0) d = √81 d = 9

Therefore, the length of the line segment that connects the points (7, 2) and (-2, 2) is 9 units.

Is the Line Segment Horizontal or Vertical?

To determine whether the line segment is horizontal or vertical, we need to examine the coordinates of the endpoints.

Horizontal Line Segment

A horizontal line segment has the same y-coordinate for both endpoints. In this case, the y-coordinate is 2 for both endpoints (7, 2) and (-2, 2). Therefore, the line segment is horizontal.

Vertical Line Segment

A vertical line segment has the same x-coordinate for both endpoints. In this case, the x-coordinate is not the same for both endpoints (7, 2) and (-2, 2). Therefore, the line segment is not vertical.

Conclusion

In conclusion, finding the length of a line segment is an essential concept in mathematics. We can use the distance formula to find the length of a line segment given its endpoints. In this article, we discussed how to find the length of a line segment and determined whether it is horizontal or vertical. We also provided an example to illustrate the concept.

Frequently Asked Questions

Q: What is a line segment?

A: A line segment is a part of a line that is bounded by two distinct points.

Q: How do I find the length of a line segment?

A: You can use the distance formula to find the length of a line segment.

Q: What is the distance formula?

A: The distance formula is given by d = √((x2 - x1)² + (y2 - y1)²).

Q: Is the line segment horizontal or vertical?

A: To determine whether the line segment is horizontal or vertical, you need to examine the coordinates of the endpoints.

Q: What is the length of the line segment that connects the points (7, 2) and (-2, 2)?

A: The length of the line segment that connects the points (7, 2) and (-2, 2) is 9 units.

References

[1] "Geometry" by Michael Artin
[2] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
[3] "Calculus" by Michael Spivak

Glossary

Line segment: A part of a line that is bounded by two distinct points.
Vertices: The endpoints of a line segment.
Distance formula: A formula used to find the length of a line segment.
Horizontal line segment: A line segment that has the same y-coordinate for both endpoints.
Vertical line segment: A line segment that has the same x-coordinate for both endpoints.