Calculator Use
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Use this calculator to calculate the midpoint, the distance between 2 points, or find an endpoint given the midpoint and the other endpoint.
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Midpoint and Endpoint Calculator Solutions
Input two points using numbers, fractions, mixed numbers or decimals. The midpoint calculator shows the work to find:
- Midpoint between two given points
- Endpoint given one endpoint and midpoint
- Distance between two endpoints
The calculator also provides a link to the Slope Calculator that will solve and show the work to find the slope, line equations and the x and y intercepts for your given two points.
How to Calculate the Midpoint
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You can find the midpoint of a line segment given 2 endpoints, (x1, y1) and (x2, y2). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint.
Calculate the midpoint, (xM, yM) using the midpoint formula:
It’s important to note that a midpoint is the middle point on a line segment. A true line in geometry is infinitely long in both directions. But a line segment has 2 endpoints so it is possible to calculate the midpoint. A ray has one endpoint and is infinitely long in the other direction.
Example: Find the Midpoint
Say you know two points on a line segment and their coordinates are (6, 3) and (12, 7). Find the midpoint using the midpoint formula.
- First, add the x coordinates and divide by 2. This gives you the x-coordinate of the midpoint, xM
- Second, add the y coordinates and divide by 2. This gives you the y-coordinate of the midpoint, yM
- Take each result to get the midpoint. In this example the midpoint is (9, 5).
How to Calculate Distance Between 2 Points
If you know the endpoints of a line segment you can use them to calculate the distance between the 2 points. Here you’re actually finding the length of the line segment. Use the formula for distance between 2 points:
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The formula for distance between points is derived from the Pythagorean theorem, solving for the length of the hypotenuse. See our Pythagorean Theorem Calculator for a closer look.
Example: Find the Distance Between 2 Points
You know 2 points on a line segment and their coordinates are (13, 2) and (7, 10). Find the distance between the 2 points using the distance formula ( d = sqrt {(x_{2} – x_{1})^2 + (y_{2} – y_{1})^2} )
- Insert your points (13, 2) and (7, 10) into the distance equation
- Complete the subtraction first since they’re in parentheses
- Find the square of each term
- Add the results
- Find the square root and you’ve found the distance between the 2 points
Similar to this midpoint calculator is our Two Dimensional Distance Calculator. For distance between 2 points in 3 dimensions with (x, y, z) coordinates please see our 3 Dimension Distance Calculator.
How to Calculate Endpoint
If you know an endpoint and a midpoint on a line segment you can calculate the missing endpoint. Start with the midpoint formula from above and work out the coordinates of the unknown endpoint.
- First, take the midpoint formula:
- And break it down so you have separate equations for the x and y coordinates of the midpoint
- Rearrange each equation so that you’re solving for x2 and y2
- Since you know the midpoint, insert its coordinates in place of xM and yM in each equation
- Insert the coordinates of your known endpoint into the values for x1 and y1
- Finally, solve each equation to find x2 and y2 which will be the coordinates of your missing endpoint
Example: Find the Endpoint
Using the steps above, let’s find the endpoint of a line segment where we know one endpoint is (6, -4) and the midpoint is (1, 7). The endpoint is the (x1, y1) coordinate. The midpoint is the (xM, yM) coordinate.
- First, take the midpoint formula:
- And rearrange the equations so that you’re solving for x2 and y2
- Insert the coordinates of your midpoint (1, 7) in place of xM and yM in each equation
- Insert the coordinates of your known endpoint (6, -4) into the values for x1 and y1
- Solve each equation to find x2 and y2.
- Your missing endpoint (x2, y2) is (-4, 18)
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