Where this calculation appears
It completes symmetric segments in coordinate geometry, graphics, construction, and reflection problems.
Math calculator
Endpoint Calculator
Recover one endpoint from a midpoint and the other endpoint. The displayed missing endpoint includes enough working to inspect signs and scale.
Endpoint inputs
Numerical setup
A numerical walkthrough
Midpoint (5,4) and known endpoint (1,−2) give missing endpoint (9,10).
What the formula is measuring
Because midpoint coordinates average endpoints, the missing endpoint is (2mₓ−x₁,2mᵧ−y₁).
The roles assigned to midpoint x, midpoint y, known endpoint x₁ and known endpoint y₁ explain the operation that produces missing endpoint.
Details to check in Endpoint
Coordinate units and axes must match. The formula assumes the supplied point is exactly the midpoint, not another division ratio. If the Endpoint assumptions do not fit, consider verify the midpoint.
When endpoint looks surprising, restore the sample and vary known endpoint x₁ by itself.
Manual method
Double each midpoint coordinate and subtract the corresponding known endpoint coordinate. To continue from Endpoint, try unequal division.
What changes—and what does not
Write each source value under its matching label before calculating: midpoint x, midpoint y, known endpoint x₁ and known endpoint y₁. This preserves the assumptions behind missing endpoint and makes a later check possible without reopening the original problem.
Moving the midpoint by one unit moves the recovered endpoint by two units when the known endpoint stays fixed. This relationship remains useful even when the final missing endpoint is rounded.
Before publishing or sharing missing endpoint, decide on units, significant digits, and whether an exact form is expected. Those choices belong to interpretation rather than the calculator engine.
The midpoint calculator averages two endpoints; this page reverses that averaging operation. The two results may share inputs while retaining different meanings.
When reporting the answer, state the missing endpoint first, then its value and unit. Add midpoint x, midpoint y, known endpoint x₁ and known endpoint y₁ if someone else must verify the work independently.
Independent check for Endpoint
Average the recovered endpoint with the known endpoint coordinate by coordinate. The result must return the supplied midpoint exactly.
For Endpoint, keep the original inputs beside this check and perform it with unrounded working values. Agreement after independent operations is stronger evidence than matching the displayed decimal places alone. If the check fails, revisit input roles, angle units, and the exact formula before changing the rounding.
Questions about Endpoint
How do I check the result?
Average the known and recovered endpoints.
Does endpoint order matter?
No; either endpoint can be the known one.
Why multiply the midpoint by two?
It reverses division by two in the midpoint formula.
Can coordinates be negative?
Yes.