{"uid":"cap_-Ie4fi8a5DB_WQthjgqNh","slug":"coordinate-geometry-solver-8d816ce9","name":"Coordinate Geometry Solver","description":"Plane geometry from coordinates: line through two points, distance, circle through three points, polygon area, intersections.","url":"https://math-geometry.x402tookit.com/coordinate-geometry?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"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":["null","number"]},"y":{"type":["null","number"]}}},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"xIntercept":{"type":["null","number"]},"yIntercept":{"type":["null","number"]},"generalForm":{"type":["null","object"],"properties":{"A":{"type":["null","number"]},"B":{"type":["null","number"]},"C":{"type":["null","number"]}}},"segmentLength":{"type":["null","number"]},"perpendicularSlope":{"type":["null","number"]},"perpendicularBisector":{"type":["null","string"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_DvW4SuMCk4V144-Yjimgh","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves plane geometry problems from coordinates: line equations, distances, circles through three points, polygon areas, and line intersections.","exampleAgentPrompt":"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?","exampleUseCases":[{"title":"Finding circle from three GPS points","prompt":"I have three coordinate points: (1, 2), (4, 6), and (7, 2) — can you find the equation of the circle that passes through all three of them, including the center and radius?"},{"title":"Computing area of land parcel","prompt":"I have a plot of land whose corners are at coordinates (0,0), (10,0), (10,5), (5,8), and (0,5) — what's the area of this polygon?"},{"title":"Finding road intersection coordinates","prompt":"Two roads run as straight lines: one goes from (1,1) to (4,5) and another from (2,4) to (6,1). Where exactly do they intersect?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T13:11:25.817Z","isFirstParty":false,"canonicalSlug":"coordinate-geometry-solver-8d816ce9"}