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How Do You Find the Midpoint Between Two Coordinates?

Find the coordinates of the midpoint of the line segment with endpoints (3,4) and (2,2).

Summary

  1. A line segment is a finite part of a line that is defined on each end by endpoints
  2. Here the endpoints are (3,4) and (2,2)
  3. The midpoint is the point that lies midway between the two endpoints
  4. The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints
  5. The y-coordinate of the midpoint is the average of the y-coordinates of the endpoints
  6. (2.5,3) lies midway in between (3,4) and (2,2)

Notes

    1. A line segment is a finite part of a line that is defined on each end by endpoints
    2. The endpoints are the points at each end of the segment that mark where it begins and ends
    1. The endpoints are the points at each end of the segment that mark where it begins and ends
    1. You can see on the graph that our line segment connects the two points (3,4) and (2,2)
    2. So (3,4) and (2,2) are the endpoints of this line segment
    1. Since we have two ordered pairs, we want to label the coordinates of each so we can use them in our formula later
    2. We'll label the x-coordinate of our first ordered pair, 3, as x1
    3. And we'll label the y-coordinate of our first ordered pair, 4, as y1
    4. Then we'll label the x-coordinate of our second ordered pair, 2, as x2
    5. And we'll label the y-coordinate of our second ordered pair, 2, as y2
    1. We can use the midpoint formula to find the coordinates for the midpoint of our line segment
    2. The midpoint formula just takes the average of the x-coordinates and the y-coordinates of the endpoints
    3. This will give us the x- and y-coordinates of the point exactly in the middle of the two endpoints
    1. (x,y)midpoint is the ordered pair for the point on the line segment that is exactly in between the two endpoints
    2. (x1+x2)/2 is the formula for the x-coordinate of the midpoint
    3. We are just taking the average of the x-coordinates of the endpoints
    4. (y1+y2)/2 is the formula for the y-coordinate of the midpoint
    5. We are just taking the average of the y-coordinates of the endpoints
    1. Remember, in Step 1 we labeled the coordinates of our endpoints (x1, y1) and (x2, y2)
    2. Now we can plug our values into the midpoint formula to find the midpoint of our line segment
    3. We have x1=3, y1=4, x2=2, and y2=2
    1. The x-coordinate of the midpoint is just the average of the x-coordinates of the endpoints
    2. So take our two x-coordinates, 3 and 2, add them together, and divide by 2
    3. This gives us 5/2, or 2.5
    1. The y-coordinate of the midpoint is just the average of the y-coordinates of the endpoints
    2. So take our two y-coordinates, 4 and 2, add them together, and divide by 2
    3. This gives us 6/2, or 3
    1. 3+2=5
    2. 5/2=2.5
    3. So 2.5 is the x-coordinate of the midpoint
    4. 4+2=6
    5. 6/2=3
    6. So 3 is the y-coordinate of the midpoint
    1. The point on the line segment that lies halfway between (3,4) and (2,2) is (2.5,3)
    2. So this is our midpoint
    1. When we plot the midpoint on the graph, it should be on the line segment exactly in between the two endpoints
    1. (2.5,3) lies right in the middle of (3,4) and (2,2), so we know that it is in fact our midpoint