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Find the Missing Endpoint from a Midpoint — result sheet
Find the second endpoint of a line segment when one endpoint and the midpoint are known, with length and slope checks.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: x₂ = 2xₘ − x₁; y₂ = 2yₘ − y₁; length = √((x₂ − x₁)² + (y₂ − y₁)²).
The midpoint is the average of the two endpoint coordinates. Rearranging each coordinate equation gives the missing endpoint, after which distance and slope provide useful geometric checks.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Known endpoint x₁ — minimum -1000000000; maximum 1000000000
- Known endpoint y₁ — minimum -1000000000; maximum 1000000000
- Midpoint x-coordinate — minimum -1000000000; maximum 1000000000
- Midpoint y-coordinate — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Known endpoint x₁ | -5 |
| Known endpoint y₁ | -4 |
| Midpoint x-coordinate | 1 |
| Midpoint y-coordinate | -1 |
Missing endpoint (7, 2), segment length 13.42
Assumptions and limits
- The points are Cartesian coordinates in one common two-dimensional coordinate system.
- The supplied midpoint is the exact midpoint of the segment rather than a rounded measurement.
- A vertical segment has an undefined slope, which is reported instead of dividing by zero.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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