Content

• Steps
• Method 1 of 2: Formula for finding the midpoint of a line segment
• Method 2 of 2: Finding the Midpoint of a Vertical or Horizontal Line
• What do you need
• Additional articles

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

Steps

Method 1 of 2: Formula for finding the midpoint of a line segment

1. 1 Definition. The midpoint of a line segment is a point that is equidistant from the endpoints of the line segment and lies on it. Thus, its coordinates are the average of two x coordinates and two y coordinates.
2. 2 Formula. The formula is written as the sum of two x coordinates (end points) divided by two and the sum of two y coordinates (end points) divided by two. This will give the average of the x and y coordinates. Formula:[(x₁ + x₂) / 2, (y₁ + y₂)/2]
3. 3 Find the coordinates of the end points. You cannot use a formula without knowing the x and y coordinates of the end points. For example, you need to find the midpoint (point O) of the segment bounded by points M (5,4) and N (3, -4). Thus, (x₁, y₁) = (5, 4) and (x₂, y₂) = (3, -4).
   • Note that any pair of coordinates can be denoted as (x₁, y₁) or (x₂, y₂).Since you'll just be adding the coordinates and dividing the result by two, it doesn't matter which pair of coordinates you pick first.
4. 4 Plug in the coordinates into the formula. Now that you know the coordinates of the end points, plug them into the formula. Here's how to do it:
   • [(5 + 3)/2, (4 + -4)/2]
5. 5 Decide. After you have substituted the coordinates in the formula, do the arithmetic to calculate the midpoint. Here's how to do it:
   • [(5 + 3)/2, (4 + -4)/2] =
   • [(8/2), (0/2)] =
   • (4, 0)
   • The midpoint between points (5,4) and (3, -4) is point (4,0).

Method 2 of 2: Finding the Midpoint of a Vertical or Horizontal Line

1. 1 Consider a vertical or horizontal line.
   • The line is horizontal if the two y-coordinates of the endpoints are equal. For example, a line segment with ends (-3, 4) and (5, 4) is horizontal.
   • The line is vertical if the two x-coordinates of the endpoints are equal. For example, a line segment with ends (2, 0) and (2, 3) is in a vertical position.
2. 2 Find the length of the line. Here's how to do it:
   • The length of the horizontal line with the end points (-3, 4) and (5, 4) is 8. You can find this by adding the absolute values ​​of the x coordinates: | -3 | + | 5 | = 8.
   • The length of the vertical segment with the end points (2, 0) and (2,3) is 3. You can find this by adding the absolute values ​​of the y coordinates: | 0 | + | 3 | = 3.
3. 3 Divide the length of the line by two. Now that you have found the length of the segment, you need to divide it by two.
   • 8/2 = 4
   • 3/2 = 1,5
4. 4 Calculate the coordinates of the middle. Here's how to do it:
   • To find the midpoint of the line segment bounded by points (-3.4) and (5.4), add or subtract 4 from the x-coordinate of the first or second endpoint, respectively. For point (-3, 4) it will be -3 + 4 = 1 and the coordinates of the middle: (1, 4) (You do not need to change the y-coordinates, since the line is horizontal and the y-coordinates are constant). So, the midpoint of the segment (-3.4) and (5.4) is the point (1.4).
   • To find the midpoint of the line segment bounded by points (2,0) and (2,3), add or subtract 1.5 from the y-coordinate of the first or second endpoint, respectively. For point (2, 0) it will be -0 + 1.5 = 1.5 and the coordinates of the middle: (2,1,5) (You don't need to change the x-coordinates, since the line is vertical and the x-coordinates are constant). So, the midpoint of the segment (2, 0) and (2,3) is the point (2,1,5).

What do you need

• Pencil
• Paper
• Ruler

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