What are three examples of line segments?

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Lines, line segments, and rays are found everywhere in geometry. Using these simple tools, you can create parallel lines, perpendicular bisectors, polygons, and so much more. In this lesson, you will learn the definitions of lines, line segments, and rays, how to name them, and few ways to measure line segments.

Line Segment

A line segment is 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, like CX¯:

You symbolize a line segment on drawing paper by using a straightedge to make a line and placing two dots at its ends, identified with capital letters; these are the endpoints of a line segment:

What is a line?

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

Straight Line Symbol

In geometry, the straight line symbol is a line segment with two arrowheads at its ends, like 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:

Rays

A ray is 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.

A ray is named using its endpoint first, and then any other point on the ray. In this example, we have Point B and Point A (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 segment CX¯, but we have added two points along the way, Point G and Point R:

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

7 units line segment CG

5 units line segment GR

3 units line segment RX

7 + 5 + 3 = 15 units of length for CX¯

Coordinate Plane

A coordinate plane, also called a Cartesian 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:

To determine line segment LM¯'s length, we start at Point L and count to our right five units, ending at Point M. You can also subtract the x-values: 8 - 3 = 5. For vertical lines, you would subtract y-values.

When working in or across Quadrants II, III and IV, recall that subtracting a negative number really means adding a positive number.

How to Find the Legnth of a Diagonal Line Segment on a Coordinate Plane

Use the Pythagorean Theorem to calculate line segment lengths of diagonals on coordinate planes. Recall that the Pythagorean Theorem is a2 + b2 = c2 for 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:

Count units straight down from Point J to the x-value 2 (which lines up with Point L):

8 - 2 = 6, so line segment JK¯ = 6

Count units straight across from Point K to Point L:

6 - (-3) = 9, so line segment KL¯ = 9

Now we have 62 + 92 = c2:

36 + 81 = c2

117 = c2

10.816 = c

The length of line segment JL¯ is approximately 10.816 units.

The Distance Formula

A special case of the Pythagorean Theorem is the Distance 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:

D = (x2 - x1)2 + (y2 - y1)2

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 (x2 - x1) is read as the change in x and (y2 - y1) is the change in y.

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

The Distance Formula makes this an easy calculation:

D = (-2 - 6)2 + (3 - 9)2

D = (-8)2 + (-6)2

D = 64 + 36

D = 100

D = 10

Using the Distance Formula, we find that line segment PI¯ = 10 units.

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.

Next Lesson:

Straight Lines

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions. In this lesson, we will learn more about a line segment, its symbol, and the way to measure a line segment.

What is a Line Segment?

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure given below shows a line segment AB, where the length of line segment AB refers to the distance between its endpoints, A and B.

Line Segment Symbol

A line segment is represented by a bar on top which is the line segment symbol. It is written as \(\overline{AB}\).

How to Measure Line Segments?

Line segments can be measured with the help of a ruler (scale). Let us see how to measure a given line segment and name it PQ.

• Step 1: Place the tip of the ruler carefully so that zero is placed at the starting point P of the given line segment.
• Step 2: Now, start reading the values given on the ruler and spot the number which comes on the other endpoint Q.
• Step 3: Thus, the length of the line segment is 4 inches, which can be written as \(\overline{PQ}\) = 4 inches.

Line Segment Formula

In the above example, we measured the length of line segment PQ to be 4 inches. This is written as \(\overline{PQ}\) = 4 inches. Now, let us see how to find the length of a line segment when the coordinates of the two endpoints are given. In this case, we use the distance formula, that is, D = √[(\(x_{2}-x_{1}\))2 + (\(y_{2}-y_{1}\))2]. Here, (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) are the coordinates of the given points.

For example, a line segment has the following coordinates: (-2, 1) and (4, –3). Let us apply the distance formula to find the length of the line segment. Here, \(x_{1}\) = -2; \(x_{2}\) = 4; \(y_{1}\) = 1; \(y_{2}\) = -3. After substituting these values in the distance formula we get: D =√[(4-(-2))2 + (-3-1)2) = √((4+2)2 + (-3-1)2] = √(62 + (-4)2) = √(36 + 16) = √52 = 7.21 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (-2, 1) and (4, –3) is 7.21 units.

Difference Between Line, Line Segment, and Ray

Observe the figures given below to understand the difference between a line, a line segment, and a ray.

Important Notes

• A line has indefinite ends and cannot be measured.
• A line segment has a start point and an endpoint, thus, it can be measured.
• Line segments have a defined length, hence, they form the sides of any polygon.
• A ray has just one start point and no endpoint, therefore, it cannot be measured.
• The concept of rays can be understood with the example of the rays of the sun, which have a beginning point but no endpoint.

☛Topics Related

Check out the following pages related to the line segment.

1. Example 1: Identify if the given figure is a line segment, a line, or a ray.

   

   Solution:

   The figure has one starting point but an arrow on the other end. This shows that it is not a line segment or a line, it is a ray. Therefore, LM is a ray.

2. Example 2: Name the line segments in the given triangle.

   

   Solution:

   The line segments which make up the triangle are \(\overline{PQ}\), \(\overline{QR}\), and \(\overline{PR}\).
   Therefore, the line segments in the given triangle are \(\overline{PQ}\), \(\overline{QR}\), and \(\overline{PR}\).

3. Example 3: Find the length of the line segment PQ if the coordinates of P and Q are (3, 4) and (2, 0) respectively.

   Solution:

   The coordinates of P and Q are (3, 4) and (2, 0). Let us apply the distance formula: D = √[(\(x_{2}-x_{1}\))2 + (\(y_{2}-y_{1}\))2]. Here, \(x_{1}\) = 3; \(x_{2}\) = 2; \(y_{1}\) = 4; \(y_{2}\) = 0. Therefore, the length of the line segment, D =√[(2-3)2+(0-4)2] = √((-1)2+(-4)2) = √(1 + 16) = √17 = 4.123 units.
   Therefore \(\overline{PQ}\) = 4.123 units.

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FAQs on Line Segment

A line segment is a part of a line that connects two points which are considered to be its endpoints. It is the distance between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

What is the Difference Between a Line and a Line Segment?

A line has no endpoints and can be extended in both ends, whereas, a line segment has two fixed endpoints, and a ray has just one starting point but no endpoint.

How to Draw a Line Segment?

To construct a line segment of any length, there are mainly two methods. One is using a ruler and the other is using a ruler and a compass. The first method of constructing a line segment is simple in which we take a ruler (scale) and mark the starting point as P, then we need to mark the endpoint as Q, with the required length of the line segment. For example, if the required length is 4 inches, we mark Q at 4 inches with the help of the ruler. After this step, the two points are joined together which shows the line segment of the desired length. Visit the Methods to Draw a Line Segment page for a detailed explanation.

What is the Midpoint of a Line Segment?

The midpoint of a line segment refers to a point that divides it into two equal parts and is located in the middle of the line segment.

How to Find the Midpoint of a Line Segment?

The midpoint of a line segment can be calculated if the coordinates of the endpoints are given. For example, if (x1, y1) and (y1, y2) are the two endpoints, then the midpoint of the line segment can be calculated by the formula, Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

What are the Examples of Line Segments in Real Life?

We know that line segments have a fixed length or measure. Thus, the examples of line segments in real life include sides of a polygon, edges of a ruler, edges of a paper, etc.

What is the Symbol of a Line Segment?

A line segment is denoted by a bar on top (—) like \(\overline{AB}\). This bar is considered as the line segment symbol.

How to Find the Length of a Line Segment?

In order to find the length of a line segment, we use a scale (ruler) to measure its dimensions. In some cases, if the coordinates of the endpoints of the line segment are given, then we apply the distance formula, D = √[(\(x_{2}-x_{1}\))2 + (\(y_{2}-y_{1}\))2], where "D" is the distance between the endpoints of the line segment and (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) are the coordinates of the two points.

When are Line Segments Congruent?

Two figures are said to be congruent if they are of the same size and shape. Thus, any two line segments can be considered to be congruent if they are of the same length.

Can a Line Segment be Extended?

No, a line segment cannot be extended because it has a fixed and definite length. Although a line can be extended in two opposite directions indefinitely, and a ray can also be extended from one end.