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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:
![What is a Line Segment? (Definition, Distance Formula, Example) (1) What is a Line Segment? (Definition, Distance Formula, Example) (1)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-line-segment-definition-in-geometry.jpg)
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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. 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:
![What is a Line Segment? (Definition, Distance Formula, Example) (2) What is a Line Segment? (Definition, Distance Formula, Example) (2)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-definition-of-a-line-in-math.jpg)
Rays
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) What is a Line Segment? (Definition, Distance Formula, Example) (3)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-definition-of-a-ray-in-math.jpg)
A ray is named using its endpoint first, and then any other point on the ray. In this example, we have PointBand PointA(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, but we have added two points along the way, PointGand PointR:
![What is a Line Segment? (Definition, Distance Formula, Example) (4) What is a Line Segment? (Definition, Distance Formula, Example) (4)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-line-segment-formula.jpg)
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
7+5+3=15
That's a total of 15 units of length for 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) What is a Line Segment? (Definition, Distance Formula, Example) (5)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-find-length-of-line-segment-on-coordinate-plane.jpg)
To determine the length of line segmentLM, we start at PointLand count to our right five units, ending at PointM. You can also subtract the x-values:
8−3=5
. 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=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:
![What is a Line Segment? (Definition, Distance Formula, Example) (6) What is a Line Segment? (Definition, Distance Formula, Example) (6)](https://i0.wp.com/static.tutors.com/assets/images/content/tutors-calculate-diagonals-using-pythagorean-theorem.jpg)
Count units straight down from PointJto the x-value2(which lines up with PointL):
8−2=6
So, line segment JK=6
Count units straight across from PointKto PointL:
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 approximately10.816units.
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:
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 asthe change in xand(y2−y1)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:
D=(−2−6)2+(3−9)2
D=(−8)2+(−6)2
D=64+36
D=100
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D=10
Using the Distance Formula, we find that line segmentPI=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.