Midpoint Calculator

About Midpoint Calculator

The midpoint is the point exactly halfway between two points. Average the x-coordinates and y-coordinates separately.

How to use this calculator

1. Enter the first point as (x_1, y_1).
2. Enter the second point as (x_2, y_2).
3. Check the coordinates for sign errors, especially with negatives.
4. Use the result to find the point halfway between the two points.

The formula explained

The midpoint formula computes the average of the x-coordinates and the average of the y-coordinates. This gives the coordinates of the point exactly halfway between the two endpoints.

• \(x_1\) = the x-coordinate of the first point
• \(y_1\) = the y-coordinate of the first point
• \(x_2\) = the x-coordinate of the second point
• \(y_2\) = the y-coordinate of the second point
• M = the midpoint

Step by step method

1. Find the average of the x-values, (x_1+x_2)/2.
2. Find the average of the y-values, (y_1+y_2)/2.
3. Write the midpoint as an ordered pair (x, y).

Worked example

Problem. Find the midpoint of the segment connecting (2, 6) and (8, 10).

1. Average the x-values: (2+8)/2 = 10/2 = 5.
2. Average the y-values: (6+10)/2 = 16/2 = 8.
3. Combine the results to get the midpoint (5, 8).

Tips and common mistakes

• Be careful with negative numbers, because (-4+10)/2 = 3, not -7/2.
• The midpoint is not the same as the distance between points, it gives the center point instead.

Frequently asked questions