Use our endpoint calculator to find an endpoint of a line segment given the other endpoint and the midpoint.
Steps to Find the Endpoint
Start with the endpoint formula
Substitute the known point values in the formula and solve
How to Find the Endpoint of a Line Segment
A line segment is defined by its endpoints, which are the points on either end of the line. A line segment is a line that connects two points, which are its endpoints.
If you know one endpoint, then you can find the other endpoint, but you’ll need some additional information. You will need to know the length of the line and its slope or the midpoint of the line segment.
Given one of the line segment’s endpoints and its midpoint, you can find the other endpoint using a simple formula.
The formula to find the coordinates of the endpoint (x2, y2) of a line segment using the other endpoint (x1, y1) and the midpoint (xm, ym) is:
This can be simplified to:
Thus, the x-coordinate of the endpoint x2 is equal to 2 times the x-coordinate of the midpoint xm minus the x-coordinate of the other endpoint x1. Similarly, the y-coordinate of the endpoint y2 is equal to 2 times the y-coordinate of the midpoint ym minus the y-coordinate of the other endpoint y1.
So, the coordinates of the endpoint can be expressed as:
You can find the midpoint to use in this formula with our midpoint calculator.
For example, let’s find the missing endpoint of a line segment with one endpoint (3, 5) and a midpoint (9, 7).
So, the missing endpoint of this line segment is (15, 9).
You may also be interested in our distance calculator to find the distance between the endpoints.