Description
Use scaled coordinates and a normalized B-to-C direction to project A onto its supporting line, returning parameter and foot coordinates.
Triangle identities relate side lengths, angles, and special points under a nondegenerate geometric model. A contribution to a point or a local ratio is different from constructing the complete point or proving that supplied values form a triangle.
Use scaled coordinates and a normalized B-to-C direction to project A onto its supporting line, returning parameter and foot coordinates.
When to use this tool
Use Triangle Altitude Foot Parameter when you need an explicit triangle identity or local construction.
How to use the tool and how it works
- Enter ax, ay, bx, by, cx, cy. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read parameter, footX, footY. Use the output convention below.
Require B and C distinct and a numerically representable side direction. Use scaled coordinates and a normalized B-to-C direction to project A onto its supporting line, returning parameter and foot coordinates.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ax | Ax | Required. Finite number. |
| ay | Ay | Required. Finite number. |
| bx | Bx | Required. Finite number. |
| by | By | Required. Finite number. |
| cx | Cx | Required. Finite number. |
| cy | Cy | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| parameter | Parameter | Required. Finite number. |
| footX | Foot X | Required. Finite number. |
| footY | Foot Y | Required. Finite number. |
{
"input": {
"ax": 1,
"ay": 3,
"bx": 0,
"by": 0,
"cx": 4,
"cy": 0
},
"output": {
"parameter": 0.25,
"footX": 1,
"footY": 0
}
}Limitations and assumptions
- Parameter zero is B and one is C; values outside [0, 1] are allowed because this is the altitude foot on the full line, without triangle-validity, tolerance, or segment clamping.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Construct the triangle from coordinates or solve the complete geometric constraints when consistency matters. Match side ordering, angle units, and internal-versus-external conventions to the intended identity.
References
Similar or alternative tools
- Geometry: Triangle Angle Bisector Foot
Validate three noncollinear two-dimensional vertices with A distinct from B and C.
- Triangle Excentral Angle From Internal
Require angleDegrees strictly between zero and 180 and return 90-angle/2 in degrees.