{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-point-line-plane"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-point-line-plane-01","title":{"zh-Hant":"點、線、面：在座標模型中判定點是否在直線上","en":"Points, lines and planes: deciding incidence in the coordinate model"},"summary":{"zh-Hant":"在座標平面模型 ℝ² 中，設 P=(1,2)、Q=(3,6)。判定 R=(4,8) 與 S=(2,5) 是否在通過 P、Q 的直線 L 上，並據此判定 P、Q、R 是否共線。","en":"In the coordinate-plane model ℝ², let P=(1,2) and Q=(3,6). Decide whether R=(4,8) and S=(2,5) lie on the line L through P and Q, and hence whether P, Q, R are collinear."},"mko_ids":["mko-point-line-plane"]}],"title":"概念推導導讀"}