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How Do You Find the Midpoint of Two Points on a Map If You Have the Coordinates?

The map coordinates of Ithaca, NY and St. Louis, MO are (3,4) and (2,2), respectively. Find the coordinates of the point on the map midway between the two cities.

Summary

  1. (3,4) and (2,2) are endpoints of a line segment
  2. (2,2) represents St. Louis
  3. (3,4) represents Ithaca
  4. Label the x- and y-coordinates of each of the points
  5. The coordinates of the midpoint are the average of the coordinates of the endpoints
  6. Plug in 3 for xITH, 2 for xSTL, 4 for yITH, and 2 for ySTL
  7. The midpoint is (2.5,3)
  8. (2.5,3) lies halfway between (3,4) and (2,2) on the graph

Notes

    1. The coordinates for Ithaca are represented by the ordered pair (3,4)
    2. The coordinates for St. Louis are represented by the ordered pair (2,2)
    1. The points for our two cities are the endpoints of a line segment
    2. A line segment is two endpoints and all the points in between them
    1. The points for our two cities are the endpoints of a line segment
    2. A line segment is two endpoints and all the points in between them
    1. Since St. Louis is represented by the point (2,2), we can label this on our graph as STL
    1. Since Ithaca is represented by the point (3,4), we can label this on our graph as ITH
    1. Labeling these coordinates now will make it easier when we use a formula to find the midpoint later
    1. We can label 3 as xITH to indicate that it is the x-coordinate for Ithaca
    2. We can label 4 as yITH to indicate that it is the y-coordinate for Ithaca
    1. We can label the first 2 as xSTL to indicate that it is the x-coordinate for St. Louis
    2. We can label the second 2 as ySTL to indicate that it is the y-coordinate for St. Louis
    1. The midpoint is the point on a line segment exactly halfway between the two endpoints
    1. Fortunately, we have a formula for the midpoint that we can use!
    1. This is the same as finding the average of the two x-coordinates
    2. Do the same thing and find the average of the two y-coordinates
    3. This will give us an ordered pair that is exactly halfway between the two endpoints
    1. Remember, our endpoints were (3,4) and (2,2)
    1. xITH =3
    2. xSTL =2
    3. So the x-coordinate of the midpoint is equal to (3+2)/2
    1. yITH =4
    2. ySTL =2
    3. So the y-coordinate of the midpoint is equal to (4+2)/2
    1. 3+2=5
    2. 5/2=2.5
    3. So the x-coordinate of the midpoint equals 2.5
    1. 4+2=6
    2. 6/3=2
    3. So the y-coordinate of the midpoint equals 3
    1. Our midpoint is (2.5,3)