# Coordinate Geometry Solver

> Coordinate Geometry Solver is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Solves plane geometry problems from coordinates: line equations, distances, circles through three points, polygon areas, and line intersections.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/coordinate-geometry?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/coordinate-geometry-solver-8d816ce9
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_-Ie4fi8a5DB_WQthjgqNh

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability coordinate-geometry-solver-8d816ce9
```

Example prompt: What's the equation of the line through the points (2, 3) and (5, 11), and can you also give me the slope, y-intercept, and midpoint?

## When to prefer this

Choose this endpoint when you need fast, precise plane geometry calculations from 2D coordinate inputs — particularly line equations, circle fitting, polygon area, or intersection finding — without setting up a local math library. Ideal for AI agents that need geometry sub-computations as part of larger workflows (GIS, CAD, education, route planning). Prefer over general-purpose math endpoints when the problem is coordinate-geometry-specific.

## Known failure modes

- Missing required 'mode' query parameter returns an error
- Collinear points provided to circle-3-points mode (no unique circle exists)
- Parallel lines provided to intersect mode (no intersection)
- Malformed coordinate strings (not in 'x,y' format) cause parse errors
- Insufficient points provided for the selected mode (e.g. only one point for distance)
- Polygon with fewer than 3 vertices returns error or zero area

## How this service works

Plane geometry from coordinates: line through two points, distance, circle through three points, polygon area, intersections.

## Output

Returns a structured JSON object containing computed geometric results relevant to the chosen mode: for 'line' mode — slope, y-intercept, x-intercept, perpendicular slope, midpoint, segment length, angle in degrees, equation string, and general form coefficients (A, B, C); for 'distance' mode — the scalar distance; for 'circle-3-points' — center coordinates and radius; for 'polygon' — area; for 'intersect' — intersection point coordinates; for 'point-line' — distance from point to line. Also includes metadata fields like source, summary, and disclaimer.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "mode"
     ],
     "properties": {
      "p1": {
       "type": "string",
       "description": "Point x,y (line, distance, circle-3-points, point-line as the point)"
      },
      "p2": {
       "type": "string",
       "description": "Second point x,y (point-line: first point of the line)"
      },
      "p3": {
       "type": "string",
       "description": "Third point x,y (circle-3-points; point-line: second line point; intersect: line 2 start)"
      },
      "p4": {
       "type": "string",
       "description": "Fourth point x,y (intersect: line 2 end)"
      },
      "mode": {
       "type": "string",
       "description": "line, distance, circle-3-points, polygon, intersect or point-line"
      },
      "points": {
       "type": "string",
       "description": "Polygon vertices as x,y;x,y;x,y in order"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "slope": {
       "type": [
        "null",
        "number"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "angleDeg": {
       "type": [
        "null",
        "number"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "equation": {
       "type": [
        "null",
        "string"
       ]
      },
      "midpoint": {
       "type": [
        "null",
        "object"
       ],
       "properties": {
        "x": {
         "type": [
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/coordinate-geometry-solver-8d816ce9/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)