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Length of a Line Segment Calculator

Table of contents

What is a line segment?What is the formula for the length of a line segment?How do I find the length of a line segment with endpoints?How to use the length of a line segment calculatorMore distance-related tools!FAQs

With the length of a line segment calculator, you can instantly calculate the length of a line segment from its endpoints.

If you're not sure of what a line segment is or how to calculate the length of a segment, then you might like to read the text below. In it, you'll find:

  • What is a line segment?;
  • The formula for the length of a line segment; and
  • How to find the length of a segment with its endpoints.

What is a line segment?

If you glance around, you'll see that we are surrounded by different geometric figures. Perhaps you have a table, a ruler, a pencil, or a piece of paper nearby, all of which can be thought of as geometric figures.

If we look again at the ruler (or imagine one), we can think of it as a rectangle. In geometry, the sides of this rectangle or edges of the ruler are known as line segments. A line segment is one of the basic geometric figures, and it is the main component of all other figures in 2D and 3D.

With these ideas in mind, let's have a look at how the books define a line segment:

"A line segment is a section of a line that has two endpoints, A and B, and a fixed length. Being different from a line, which does not have a beginning or an end. The line segment between points A and B is denoted with a top bar symbol as the segment AB\overline{AB}."

Returning to the ruler, we could name the beginning of the numbered side as point A and the end as point B. According to the definition, this actually corresponds to a line segment with a beginning and an end (endpoints A and B) and a fixed length (ruler's length).

But what if the line segment we want to calculate the length of isn't the edge of a ruler? Great question! Another way to determine the length of a line segment is by knowing the position (coordinates) of its endpoints A and B.

This implies that a line segment can be drawn in a coordinate plane XY. This coordinate plane representation of a line segment is very useful for algebraically studying the characteristics of geometric figures, as is the case of the length of a line segment.

In the sections below, we go into further detail on how to calculate the length of a segment given the coordinates of its endpoints.

💡 For the sake of convenience, we referred to the endpoints of a line segment as A and B. Endpoints can be labeled with any other letters, such as P and Q, C and F, and so on.

What is the formula for the length of a line segment?

The formula for the length of a line segment is given by the distance formula, an expression derived from the Pythagorean theorem:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where:

  • d — Length of the line segment;
  • x₁ and y₁ — Coordinates of any of the endpoints of the line segment; and
  • x₂ and y₂ — Coordinates of the other endpoint.

How do I find the length of a line segment with endpoints?

To find the length of a line segment with endpoints:

  1. Use the distance formula:
    d = √[(x₂ - x₁)² + (y₂ - y₁)²]

  2. Replace the values for the coordinates of the endpoints, (x₁, y₁) and (x₂, y₂).

  3. Perform the calculations to get the value of the length of the line segment.

🙋 Not sure if you got the correct result for a problem you're working on? Replace your values in the calculator to verify your answer 😉

How to use the length of a line segment calculator

With this length of a line segment calculator, you'll be able to instantly find the length of a segment with its endpoints. To use this tool:

  1. In the First point section of the calculator, enter the coordinates of one of the endpoints of the segment, x₁ and y₁.

  2. Similarly, in the Second point section, input the coordinates' values of the other endpoint, x₂ and y₂.

  3. Finally, the calculator will display the length of the segment (Length) in the Result section.

  4. That's it! 😄

🙋 Why don't you give it a try? What is the length of a line segment with endpoints (-3,1) and (2,5)? 🤔

FAQs

What is the length of a line segment from the origin to the point (- 3, 4)?

The length of the line segment is 5. To obtain this result:

  1. Use the distance formula:
    d = √[(x₂ - x₁)² + (y₂ - y₁)²]

  2. In our example, the variables of this formula are:
    (x₁, y₁) = (0, 0)
    (x₂, y₂) = (-3, 4)

  3. Substitute and perform the corresponding calculations:
    d = √[(-3 - 0)² + (4 - 0)²]
    d = √[(-3)² + (4)²]
    d = √[9 + 16]
    d = √25

  4. By finding the square root of this number, you get the segment's length:
    d = 5

Distance between endpoints of a line segment

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