What space Lines, line Segments, and also Rays?

Lines, heat segments, and also rays are uncovered everywhere in geometry. Utilizing these simple tools, you can develop parallel lines, perpendicular bisectors, polygons, and so much more. In this lesson, friend will find out the definitions of lines, heat segments, and also rays, exactly how to name them, and few ways to measure line segments.

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Table of Contents

Line SegmentWhat is a line?Measuring line Segments

Line Segment

A line segment is a section or item of a line that enables you to develop polygons, recognize slopes, and also make calculations. Its size is finite and also is identified by its two endpoints.

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

Line Segment Symbol

You surname a line segment through its two endpoints. The shorthand because that a heat segment is to create the line segments 2 endpoints and also draw a dash over them, prefer CX¯:

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You symbolize a heat segment top top drawing record by making use of a straightedge to make a line and also placing two dots in ~ its ends, established with resources letters; these space the endpoints of a line segment:

What is a line?

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

Straight heat Symbol

In geometry, the right line price is a heat segment through two arrowheads at its ends, choose CX↔. You recognize it v two called points, shown by resources letters. Pick a point on the line and give the a letter, then pick a second; currently you have actually the surname of your line:

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Rays

A ray is a component of a heat that has one endpoint and also goes ~ above infinitely in only one direction. You cannot measure the size of a ray.

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A ray is called using its endpoint first, and then any kind of other allude on the ray. In this example, we have suggest B and suggest A (BA→).

Measuring heat Segments

A heat segment is called by the endpoints, however other points along its length can be named, too. Each section of the heat segment have the right to be labeled for length, so you can include them up to determine the complete length of the line segment.

Line Segment Example

Here we have actually line segment CX¯, yet we have added two points follow me the way, point G and point R:

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

7 systems line segment CG

5 systems line segment GR

3 units line segment RX

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

Coordinate Plane

A coordinate plane, additionally called a Cartesian plane (thank you, René Descartes!), is the grid gathered from a x-axis and also a y-axis. You can think of the as 2 perpendicular number lines, or together a map the the territory occupied by heat segments.

To identify the size of horizontal or vertical heat segments ~ above the plane, counting the individual units from endpoint come endpoint:

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To identify line segment LM¯"s length, we start at allude L and count come our right 5 units, ending at suggest M. Girlfriend can additionally subtract the x-values: 8 - 3 = 5. Because that vertical lines, you would subtract y-values.

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

How to uncover the Legnth that a Diagonal heat Segment top top a name: coordinates Plane

Use the Pythagorean Theorem to calculate line segment lengths of diagonals on name: coordinates planes. Recall that the Pythagorean to organize is a2 + b2 = c2 for any right triangle. A diagonal on a name: coordinates grid develops the hypotenuse of a best triangle, so can quickly count the devices of the 2 sides:

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Count units right down from point J come the x-value 2 (which lines increase with point L):

8 - 2 = 6, so line segment JK¯ = 6

Count systems straight throughout from allude K to allude 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 heat segment JL¯ is approximately 10.816 units.

The distance Formula

A special situation of the Pythagorean theorem is the Distance Formula, used exclusively in name: coordinates geometry. You have the right to plug in the 2 endpoint x- and also y- worths of a diagonal line and also determine the length. The formula looks like this:


To use the street Formula, take the squares of the change in x-value and also the adjust in y-value and add them, then take the sum"s square root.

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

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

The distance Formula provides this basic calculation:

D = (-2 - 6)2 + (3 - 9)2

D = (-8)2 + (-6)2

D = 64 + 36

D = 100

D = 10

Using the street Formula, we discover that heat segment PI¯ = 10 units.

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Examples of heat Segments In actual Life

Real-world examples of heat segments are a pencil, a baseball bat, the cord to her cell phone call charger, the sheet of a table, etc. Think the a real-life quadrilateral, choose a chessboard; the is make of 4 line segments. Unlike line segments, instances of heat segments in real life room endless.

Next Lesson:

Straight Lines


Lesson Summary:

After functioning your way through this lesson and also video, you must be able to:

Define and identify a directly line, heat segments, and raysConstruct line segmentsMeasure the distance in between two pointsWork through line segments on a Cartesian or name: coordinates planeApply the Pythagorean Theorem and Distance Formula to calculate lengths ~ above a coordinate plane