What is a Line Segment? (Definition, Distance Formula, Example) (2024)

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Malcolm McKinsey

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Line segment

Aline segmentis a portion or piece of a line that allows you to build polygons, determine slopes, and make calculations. Its length is finite and is determined by its two endpoints.

The line segment is a snippet of the line. No matter how long the line segment is, it is finite.

Line segment symbol

You name a line segment by its two endpoints. The shorthand for a line segment is to write the line segments two endpoints and draw a dash above them, likeCX\overline{CX}CX:

What is a Line Segment? (Definition, Distance Formula, Example) (1)

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What is a line?

The definition of alineis the set of points between and beyond two points. A line is infinite in length. All points on a line arecollinear points.

Straight line symbol

In geometry, the straight line symbol is a line segment with two arrowheads at its ends, like CX\overleftrightarrow{CX}CX. You identify it with two named points, indicated by capital letters. Pick a point on the line and give it a letter, then pick a second; now you have the name of your line:


Arayis a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

What is a Line Segment? (Definition, Distance Formula, Example) (3)

A ray is named using its endpoint first, and then any other point on the ray. In this example, we have PointBand PointA(BA\overset{\to }{BA}BA).

Measuring line segments

A line segment is named by its endpoints, but other points along its length can be named, too. Each portion of the line segment can be labeled for length, so you can add them up to determine the total length of the line segment.

Line segment example

Here we have line segmentCX\overline{CX}CX, but we have added two points along the way, PointGand PointR:

What is a Line Segment? (Definition, Distance Formula, Example) (4)

To determine the total length of a line segment, you add each segment of the line segment. The formula for the line segment CX would be: CG + GR + RX = CX

  • 7units line segmentCG

  • 5units line segmentGR

  • 3units line segmentRX


That's a total of 15 units of length for CX\overline{CX}CX.

Coordinate plane

Acoordinate plane, also called aCartesian plane(thank you, René Descartes!), is the grid built up from a x-axis and a y-axis. You can think of it as two perpendicular number lines, or as a map of the territory occupied by line segments.

To determine the length of horizontal or vertical line segments on the plane, count the individual units from endpoint to endpoint:

What is a Line Segment? (Definition, Distance Formula, Example) (5)

To determine the length of line segmentLM\overline{LM}LM, we start at PointLand count to our right five units, ending at PointM. You can also subtract the x-values:


. For vertical lines, you would subtract y-values.

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When working in or across QuadrantsII,IIIandIV, recall that subtracting a negative number really means adding a positive number.

How to find the length of a diagonal line segment on a coordinate plane

Use thePythagorean Theoremto calculate line segment lengths of diagonals on coordinate planes. Recall that the Pythagorean Theorem isa2+b2=c2{a}^{2}+{b}^{2}={c}^{2}a2+b2=c2for any right triangle.

A diagonal on a coordinate grid forms the hypotenuse of a right triangle, so can quickly count the units of the two sides:

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Count units straight down from PointJto the x-value2(which lines up with PointL):


So, line segment JK=6\overline{JK}=6JK=6

Count units straight across from PointKto PointL:


So, line segment KL=9\overline{KL}=9KL=9. Now we have 62+92=c2{6}^{2}+{9}^{2}={c}^{2}62+92=c2:




The length of line segment


is approximately10.816units10.816 units10.816units.

The distance formula

A special case of the Pythagorean Theorem is theDistance Formula, used exclusively in coordinate geometry. You can plug in the two endpoint x- and y- values of a diagonal line and determine its length. The formula looks like this:


To use the distance formula, take the squares of the change in x-value and the change in y-value and add them, then take that sum's square root.

The expression(x2x1)({x}_{2}-{x}_{1})(x2x1) is read asthe change in xand(y2y1)({y}_{2}-{y}_{1})(y2y1)isthe change in y.

Imagine we have a diagonal line stretching from PointP(6,9)to PointI(-2,3), and you want to measure the distance between the two points.

The distance formula makes this an easy calculation:





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Using the Distance Formula, we find that line segmentPI=10units\overline{PI}=10unitsPI=10units.

Examples of line segments in real life

Real-world examples of line segments are a pencil, a baseball bat, the cord to your cell phone charger, the edge of a table, etc. Think of a real-life quadrilateral, like a chessboard; it is made of four line segments. Unlike line segments, examples of line segments in real life are endless.

What is a Line Segment? (Definition, Distance Formula, Example) (2024)


What is a Line Segment? (Definition, Distance Formula, Example)? ›

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

What is the distance formula of a line segment definition? ›

What is the distance formula? The distance between two points is the length of the line segment that connects them on a plane. The formula is d = ( ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 ) , where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the coordinates of the two points.

What is the definition and example of line segment? ›

As long as a figure has two endpoints and is part of a line, it is a line segment, no matter how short or long. For example, The dime and the sailboat both have line segments.

What is the formula for line segment? ›

d =√(x2– x1)2+(y2 – y1)2, or line segment is a distance between two points, so we can also use the distance formula.

What is the formula for line distance? ›

The distance between two points is defined as the length of the straight line connecting these points in the coordinate plane. This distance can never be negative, therefore we take the absolute value while finding the distance between two given points. It is calculated by the formula √[(x2 − x1)2 + (y2 − y1)2].

What is the distance between two ends of a line segment? ›

The distance between the endpoints of a line segment is called the segment length. We use different notations to refer to the length of a segment and the segment itself.

How is a line segment defined? ›

In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints.

What are 3 types of line segments? ›

Yes , we can divide Line segment in 3 categories : Closed , Open and Half-open.
  • A closed line segment includes both endpoints.
  • An open line segment excludes both endpoints.
  • A half-open line segment includes exactly one of the endpoints.
Oct 26, 2017

What is the formula of segment? ›

Here is a list of area of segment formula class 10: Area of a Segment in Radians = A = (½) × r2 (θ – Sin θ) Area of a Segment in Degrees = A = (½) × r2 × [(π/180) θ – sin θ]

How do you identify a line segment? ›

A line segment is a line section that can link two points.

It has no endpoints and extends endlessly in both directions. If you mark two points A and B on it and pick this segment separately, it becomes a line segment. This line segment has two endpoints A and B whose length is fixed.

What is the formula for a line segment parallel? ›

Parallel lines are two (or more) coplanar lines that have the same slope. If the slope of a line is given or can be determined, a line parallel to that original line can be constructed using the same slope and counting the rise over run. Given an equation in slope-intercept form, y = m x + b the slope is equal to m.

What is the formula for segment addition and distance? ›

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.

What is the midpoint formula of a line segment definition? ›

The midpoint splits the line segment into two parts of the exact same length. The midpoint formula is ( x 1 + x 2 2 , y 1 + y 2 2 ) , where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the endpoints of the line segment.

Which line segment was the distance formula derived for? ›

Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse.

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