Situations modeled by Endpoint
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
One complete Endpoint calculation
Midpoint (5,4) and known endpoint (1,−2) give missing endpoint (9,10).
How the Endpoint rule is built
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.
Which parts of Endpoint can move
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.
Independent check for Endpoint
Average the recovered endpoint with the known endpoint coordinate by coordinate. The result must return the supplied midpoint exactly.
Double each midpoint coordinate and subtract the corresponding known endpoint coordinate. To continue from Endpoint, try unequal division.
Confirming the Endpoint setup
Substitute the Endpoint solution into Midpoint x. This Endpoint check rejects false Endpoint branches and forbidden denominators.
Choose an easy Midpoint x value before running Endpoint. Predict Midpoint y, then compare it with the Endpoint output.
Start the Endpoint cross-check with Midpoint x. Apply the original Midpoint y and recompute Missing endpoint. Treat a different Known endpoint x₁ as new Endpoint data. That prevents its Missing endpoint from being attributed to the earlier Endpoint setup.
A hand-worked reference for Endpoint need not duplicate the original numbers. Select an uncomplicated Midpoint x, retain Midpoint y, and estimate Missing endpoint. The reference gives the original Endpoint answer a meaningful scale check.
Validating Endpoint
Test a boundary relevant to Midpoint x during the Endpoint review. Hold Midpoint y constant and anticipate Missing endpoint. The boundary case can reveal a branch or limit hidden by the original Endpoint numbers.
A final Endpoint check
Keep the input convention with Missing endpoint so a later Endpoint review does not assign the number a different meaning.
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.