How To Find The Midpoint Of A Line Segment: 9 Steps - WikiHow

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Terms of Use wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow How to Find the Midpoint of a Line Segment PDF download Download Article Explore this Article methods 1 Use the Midpoint Formula 2 Find the Midpoint of Vertical or Horizontal Lines Other Sections Questions & Answers Video Things You'll Need Related Articles Expert Interview References Article Summary Co-authored by Kevin Wang

Last Updated: September 17, 2024 References

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This article was co-authored by Kevin Wang. Kevin Wang is a Math Tutor based in New York, New York. Kevin has been tutoring math for over 10 years, and specializes in K-12 math topics and standardized tests, such as SAT and ACT. Kevin has an economics background and a career in both finance and marketing analytics. His interest in tutoring goes back even longer than his career. He discovered tutoring at the start of his university career and enjoys it as a way to stay sharp with fundamental skills and remain up to date with trends in our education system. Kevin received a BS in Economics from Duke University. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been viewed 177,713 times.

Finding the midpoint of a line segment is easy as long as you know the coordinates of the two endpoints. The most common way to do this is to use the midpoint formula, but there's another way to find the midpoint of a line segment if it's vertical or horizontal. If you want to know how to find the midpoint of a line segment in just a few minutes, just follow these steps.

Steps

Method 1 Method 1 of 2:

Use the Midpoint Formula

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  1. Step 1 Understand the midpoint. 1 Understand the midpoint. The midpoint of a line segment is the point that is located on the exact midpoint of the two endpoints. Therefore, it's the average of the two endpoints, which is the average of the two x-coordinates and the two y-coordinates.[1] [2]
  2. Step 2 Learn the midpoint formula. 2 Learn the midpoint formula. The midpoint formula can be used by adding the x-coordinates of the two endpoints and dividing the result by two and then adding the y-coordinates of the endpoints and dividing them by two.[3] [4] This is how you will find the average of the x and y coordinates of the endpoints.[5] This is the formula: [(x1 + x2)/2,( y1 + y2)/2] Advertisement
  3. Step 3 Locate the coordinates of the endpoints. 3 Locate the coordinates of the endpoints. You can't use the midpoint formula without knowing the x and y-coordinates of the endpoints. In this example, you want to find the midpoint, point O, which is between the two endpoints M (5,4) and N (3,-4). Therefore, (x1, y1) = (5, 4) and (x2, y2) = (3, -4).[6]
    • Note that either pair of coordinates can serve as (x1, y1) or (x2, y2) -- since you'll just be adding the coordinates and dividing by two, it doesn't matter which pair is first.
  4. Step 4 Plug the corresponding coordinates into the formula. 4 Plug the corresponding coordinates into the formula. Now that you know the coordinates of the endpoints, you can plug them into the formula. Here's how you do it:[7]
    • [(5 + 3)/2, (4 + -4)/2]
  5. Step 5 Solve. 5 Solve. Once you've plugged the appropriate coordinates into the formula, all you have to do is the simple arithmetic that will give you the midpoint of the two line segments.[8] Here's how you do it:
    • [(5 + 3)/2, (4 + -4)/2] =
    • [(8/2), (0/2)] =
    • (4, 0)
    • The midpoint of the endpoints (5,4) and (3, -4) is (4,0).
    6. Advertisement
Method 2 Method 2 of 2:

Find the Midpoint of Vertical or Horizontal Lines

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  1. Step 1 Find a vertical or horizontal line. 1 Find a vertical or horizontal line. Before you can use this method, you'll need to know how to locate a vertical or horizontal line.[9] Here's how to spot it:
    • A line is horizontal if the two y-coordinates of the endpoints are equal. For example, the line segment with the endpoints (-3, 4) and (5, 4) is horizontal.Step 1 Find a vertical or horizontal line.
    • A line is vertical if the two x-coordinates of the endpoints are equal. For example, the line segment with the endpoints (2, 0) and (2, 3) is vertical.Step 1 Find a vertical or horizontal line.
  2. Step 2 Find the length of the segment. 2 Find the length of the segment. You can easily find the length of the segment just by counting how many horizontal spaces it takes up if it's horizontal, and counting how many vertical spaces it takes up if it's vertical. Here's how to do it:[10]
    • The horizontal line segment with the end points (-3, 4) and (5, 4) is 8 units long. You can find this by counting the spaces it takes up or by adding the absolute values of the x-coordinates: |-3| + |5| = 8Step 2 Find the length of the segment.
    • The vertical line segment with the end points (2, 0) and (2, 3) is 3 units long. You can find this by counting the spaces it takes up or by adding the absolute values of the y-coordinates: |0| + |3| = 3Step 2 Find the length of the segment.
  3. Step 3 Divide the length of the segment by two. 3 Divide the length of the segment by two. Now that you know the length of the line segment, you can divide it by two.[11]
    • 8/2 = 4Step 3 Divide the length of the segment by two.
    • 3/2 = 1.5Step 3 Divide the length of the segment by two.
  4. Step 4 Count that value from either of the endpoints. 4 Count that value from either of the endpoints. This is the last step to finding the endpoint of the line segment. Here's how you do it:[12]
    • To find the midpoint of the points (-3, 4) and (5, 4), just shift over 4 units either from the left or right to reach the middle of the segment. (-3, 4) shifted over 4 x-coordinates is (1, 4). You won't need to change the y-coordinates since you know the midpoint will be on the same y-coordinate as the endpoints. The midpoint of (-3, 4) and (5, 4) is (1, 4).Step 4 Count that value from either of the endpoints.
    • To find the midpoint of the points (2, 0) and (2, 3), just shift over 1.5 units either from the top or bottom to reach the middle of the segment. (2, 0) shifted up 1.5 y-coordinates is (2, 1.5). You won't need to change the x-coordinates since you know the midpoint will be on the same x-coordinate as the endpoints. The midpoint of (2, 0) and (2, 3) is (2, 1.5).Step 4 Count that value from either of the endpoints.
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Community Q&A

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  • Question How do I find the other end of the line segment if I'm given one end and the midpoint? Donagan Donagan Top Answerer The line segment extends beyond the midpoint a distance equal to the distance between the given end point and the midpoint. As a simple example, if the line segment begins at (0,0) and has a midpoint at (2,3), the line segment extends 2 x-units and 3 y-units beyond (2,3), meaning that the line segment ends at (4,6). Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 1 Helpful 9
  • Question How do I find the point that is one forth of the way from (2,4) to (10,8)? Donagan Donagan Top Answerer Solve this by inspection: the point's x-coordinate is one-quarter of the way from 2 to 10, which is 4. The point's y-coordinate is one-quarter of the way from 4 to 8, which is 5. Thus, the point's coordinates are (4,5). Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 4
  • Question What is the midpoint of a line segment with endpoint at (0,8) and (-8,0)? Donagan Donagan Top Answerer As shown in the above article, the midpoint's x-coordinate is halfway between the x-coordinates of the endpoints, 0 and -8 (i.e., -4), and the midpoint's y-coordinate is halfway between the y-coordinates of the endpoints, 8 and 0 (i.e., 4) Thus, the midpoint is located at (-4,4). Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 5
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Expert Interview

Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with Kevin Wang.

References

  1. ↑ Kevin Wang. Math Tutor. Expert Interview
  2. ↑ http://www.mathopenref.com/midpoint.html
  3. ↑ Kevin Wang. Math Tutor. Expert Interview
  4. ↑ https://www.purplemath.com/modules/midpoint.htm
  5. ↑ http://www.mathplanet.com/education/algebra-1/radical-expressions/the-distance-and-midpoint-formulas
  6. ↑ https://mathbitsnotebook.com/Geometry/CoordinateGeometry/CGmidpoint.html
  7. ↑ https://www.mathsisfun.com/algebra/line-midpoint.html
  8. ↑ https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/v/midpoint-formula
  9. ↑ https://mathbitsnotebook.com/Geometry/CoordinateGeometry/CGmidpoint.html
More References (3)
  1. ↑ https://www.khanacademy.org/math/geometry-home/geometry-lines/basic-geo-measuring-segments/v/measuring-segments
  2. ↑ https://www.calculatorsoup.com/calculators/geometry-plane/midpoint-calculator.php
  3. ↑ https://www.chilimath.com/lessons/intermediate-algebra/midpoint-formula/

About This Article

Kevin Wang Co-authored by: Kevin Wang Math Tutor This article was co-authored by Kevin Wang. Kevin Wang is a Math Tutor based in New York, New York. Kevin has been tutoring math for over 10 years, and specializes in K-12 math topics and standardized tests, such as SAT and ACT. Kevin has an economics background and a career in both finance and marketing analytics. His interest in tutoring goes back even longer than his career. He discovered tutoring at the start of his university career and enjoys it as a way to stay sharp with fundamental skills and remain up to date with trends in our education system. Kevin received a BS in Economics from Duke University. This article has been viewed 177,713 times. 38 votes - 69% Co-authors: 18 Updated: September 17, 2024 Views: 177,713 Categories: Coordinate Geometry Article SummaryX

In order to find the midpoint of a line segment, you first have to understand that it’s the point located on the exact midpoint of the 2 endpoints, so it’s the average of the endpoints. To use the midpoint formula, add the x-coordinates of the endpoints and divide the result by 2. Then, add the y-coordinates of the endpoints and divide them by 2. Once you know the coordinates of the endpoints, you can plug them into the formula and solve. To learn how to find the midpoint of the vertical and horizontal lines, keep reading! Did this summary help you?YesNo

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Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Kevin Wang Co-authored by: Kevin Wang Math Tutor 38 votes - 69% Click a star to vote Co-authors: 18 Updated: September 17, 2024 Views: 177,713 Anonymous

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