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How to Find Distances & Midpoints Between Pairs of Points

The Cartesian coordinate planes are the most common system for graphing a set of points. This system uses a horizontal x-axis and a vertical y-axis. An ordered pair defines points on the plane. You note them as "(x,y)," where "x" is the location on the x-axis and "y" is the location on the y-axis. Both values in the ordered pair can be positive or negative. Plotting points on the coordinate system can be useful in modeling everyday systems.

Instructions

  1. Finding the Midpoint of Two Points

    • 1

      Calculate the sum of the x-axis coordinates of the two points. For example, if the two points are (x1,y1) and (x2,y2), calculate x2+x1.

    • 2

      Calculate the sum of the y-axis coordinates of the two points. For example, if the two points are (x1,y1) and (x2,y2), calculate y2+y1.

    • 3

      Divide the result from Step 1 by 2 to get the x-axis value of the midpoint. Divide the result from Step 2 by 2 to get the y-axis value of the midpoint. For example, the midpoint would be ((x2+x1)/2, (y2+y1)/2).

    Finding the Distance Between Two Points

    • 4

      Calculate the difference between the x-axis coordinates of the two points. For example, if the two points are (x1,y1) and (x2,y2), calculate x2-x1.

    • 5

      Calculate the difference between the y-axis coordinates of the two points. For example, if the two points are (x1,y1) and (x2,y2), calculate y2-y1.

    • 6

      Sum the square of the value from Step 1 and the square of the value from Step 2. This value would be ((x2-x1)^2 + (y2-y1)^2).

    • 7

      Take the square root of the value from Step 3. This is the distance between the two points. In this example, the final equation would be sqrt((x2-x1)^2 + (y2-y1)^2).

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