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 ABβ€Ύ\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.

πŸ’‘ 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 = √[(xβ‚‚ - x₁)Β² + (yβ‚‚ - y₁)Β²]

where:

  • d β€” Lenght of the line segment;
  • x₁ and y₁ β€” Coordinates of any of the endpoints of the line segment; and
  • xβ‚‚ and yβ‚‚ β€” 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 = √[(xβ‚‚ - x₁)Β² + (yβ‚‚ - y₁)Β²]

  2. Replace the values for the coordinates of the endpoints, (x₁, y₁) and (xβ‚‚, yβ‚‚).

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

πŸ™‹ 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 πŸ˜‰

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, xβ‚‚ and yβ‚‚.

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

  4. That's it! πŸ˜„

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

Did you find the length of a line segment calculator useful? If you did, you might like to visit some of our other distance calculation tools:

FAQ

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 = √[(xβ‚‚ - x₁)Β² + (yβ‚‚ - y₁)Β²]

  2. In our example, the variables of this formula are:
    (x₁, y₁) = (0, 0)
    (xβ‚‚, yβ‚‚) = (-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

Gabriela Diaz
Distance between endpoints of a line segment
First point
x₁
y₁
Second point
xβ‚‚
yβ‚‚
Result
Length
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