Endpoint Calculator
Find the missing endpoint given a midpoint and one known endpoint.
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Request a ToolHow to Use the Endpoint Calculator
This tool finds the missing endpoint of a line segment when you know the midpoint and one endpoint.
- Enter the midpoint. Provide the x and y coordinates of the midpoint.
- Enter the known endpoint. Provide the x and y coordinates of the endpoint you know.
- View the result. The missing endpoint is calculated and displayed instantly.
About the Endpoint Formula
If M is the midpoint of segment AB with coordinates (mx, my), and A = (ax, ay) is the known endpoint, then the missing endpoint B = (2*mx - ax, 2*my - ay). This is derived from the midpoint formula: M = ((ax + bx)/2, (ay + by)/2). Solving for B gives the endpoint formula. This is a common problem in coordinate geometry and standardized tests.
Frequently Asked Questions
What is the endpoint formula?
The missing endpoint is (2 * midpoint_x - known_x, 2 * midpoint_y - known_y). It reverses the midpoint formula to find the unknown point.
How is the endpoint formula derived?
Start with the midpoint formula: midpoint = (A + B)/2. Multiply both sides by 2 and subtract the known endpoint to isolate B.
Does this work in 3D?
The same formula works in 3D by adding a z-coordinate. This calculator handles the 2D case.