Javascript required
Skip to content Skip to sidebar Skip to footer
Home / How to Find the Midpoint of a Line Segment

How to Find the Midpoint of a Line Segment

Download Article

Download Article

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.

  1. 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

    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.[2] This is how you will find the average of the x and y coordinates of the endpoints.[3] This is the formula: [(x1 + x2)/2,( y1 + y2)/2]

  3. 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).

    • 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. 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:

    • [(5 + 3)/2, (4 + -4)/2]

  5. 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.[4] 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).

  1. 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.[5] 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.
    • 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.

  2. 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:[6]

    • 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| = 8
    • 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| = 3

  3. 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.[7]

    • 8/2 = 4
    • 3/2 = 1.5

  4. 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:

    • 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).
    • 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).

Add New Question

  • Question

    How do I find the other end of the line segment if I'm given one end and the midpoint?

    Donagan

    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).

  • Question

    How do I find the point that is one forth of the way from (2,4) to (10,8)?

    Donagan

    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).

  • Question

    What is the midpoint of a line segment with endpoint at (0,8) and (-8,0)?

    Donagan

    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).

  • Question

    What's the midpoint of (2,8) and (10,12)?

    Community Answer

    (X1 + X2) / 2 , (Y1 + Y2) / 2 Therefore, the midpoint is (6,10)

  • Question

    How do I find the coordinates of the point A (3,-4) and B (-2,5) that is twice as far from A as from B?

    Donagan

    First of all, there is an infinite number of points on the coordinate plane that satisfy that requirement. However, considering only points on the line that connects points A and B, the required point has an x-coordinate two-thirds of the way from 3 to -2 and a y-coordinate two-thirds of the way from -4 to 5. The x-distance from 3 to -2 is 5. 2/3 of 5 is 10/3 or 3 1/3. Add 3 1/3 to 3 (the x-coordinate of A) to get 6 1/3, which is the x-coordinate of the required point. The y-distance from -4 to 5 is 9. 2/3 of 9 is 6. Add 6 to -4 (the y-coordinate of A) to get 2, which is the y-coordinate of the required point. Thus, the required point is (6 1/3, 2).

  • Question

    If the coordinates of the midpoint of the line segment with end points (a, 4) and (3, b) are (5, -2), how do I find the values of a and b?

    Donagan

    5 is the midpoint between a and 3 on the x-axis, and -2 is the midpoint between 4 and b on the y-axis. As for the x coordinates, there is a distance of 2 units from midpoint 5 to end point 3, so you would count 2 units from 5 in the other x direction (to the left), meaning the value of a is 7. As for the y coordinates, there is a distance of 6 units from midpoint -2 to end point 4, so you would count 6 units from -2 in the other y direction (down), meaning the value of b is -8.

  • Question

    What is the midpoint of a segment whose end points are (5,8) and (11,6)?

    Community Answer

    Add x values and divide by 2. This will give you the x coordinate of the midpoint. Then do the same with the y values and get the y coordinate of the midpoint. The midpoint will be (8,7).

  • Question

    What is the complementary angle of 65?

    Donagan

    The complementary angle of 65° is 25°.

  • Question

    What is the slope of a line segment?

    Donagan

    The slope is a measurement of the vertical change of a line from one point to another, compared with (divided by) its horizontal change between the same two points.

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit


Video

Thanks for submitting a tip for review!

Things You'll Need

  • Pencil
  • A sheet of paper
  • Ruler
  • Scissors
  • Calculator

About This Article

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?

Thanks to all authors for creating a page that has been read 147,772 times.

Did this article help you?

How to Find the Midpoint of a Line Segment

Source: https://www.wikihow.com/Find-the-Midpoint-of-a-Line-Segment