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Orthocenter of a 2D Triangle — result sheet
Find the Cartesian orthocenter of a non-collinear triangle from its three ordered vertices.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: H = A + B + C - 2O, where O is the circumcenter of the same non-collinear triangle.
The orthocenter is the common intersection of the three altitudes. For a non-collinear Cartesian triangle, it can be computed transparently from the vertices and their circumcenter.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vertex A x1 — The x coordinate of vertex A.; minimum -1000000; maximum 1000000
- Vertex A y1 — The y coordinate of vertex A.; minimum -1000000; maximum 1000000
- Vertex B x2 — The x coordinate of vertex B.; minimum -1000000; maximum 1000000
- Vertex B y2 — The y coordinate of vertex B.; minimum -1000000; maximum 1000000
- Vertex C x3 — The x coordinate of vertex C.; minimum -1000000; maximum 1000000
- Vertex C y3 — The y coordinate of vertex C.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vertex A x1 | 0 |
| Vertex A y1 | 0 |
| Vertex B x2 | 4 |
| Vertex B y2 | 0 |
| Vertex C x3 | 0 |
| Vertex C y3 | 3 |
The orthocenter is (0, 0), the right-angle vertex.
Assumptions and limits
- The three vertices are finite points in one two-dimensional Cartesian coordinate system and are not collinear or nearly collinear.
- The result is the Euclidean orthocenter of the triangle; altitude lines are understood in the same metric, with no unit conversion, spherical geometry, or finite-object interpretation.
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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