# Points, Lines, and Planes

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20260917-point-line-plane · 2026-09-17 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Geometric Object Role

In the explicit model, the symbol P1 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P1 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0001/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 2. Geometric Object Role

In the explicit model, the symbol l2 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l2 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0002/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 3. Geometric Object Role

In the explicit model, the symbol α3 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α3 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0003/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 4. Geometric Object Role

In the explicit model, the symbol P4 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P4 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0004/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 5. Geometric Object Role

In the explicit model, the symbol l5 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l5 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0005/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 6. Geometric Object Role

In the explicit model, the symbol α6 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α6 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0006/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 7. Geometric Object Role

In the explicit model, the symbol P7 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P7 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0007/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 8. Geometric Object Role

In the explicit model, the symbol l8 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l8 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0008/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 9. Geometric Object Role

In the explicit model, the symbol α9 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α9 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0009/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 10. Geometric Object Role

In the explicit model, the symbol P10 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P10 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0010/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 11. Geometric Object Role

In the explicit model, the symbol l11 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l11 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0011/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 12. Geometric Object Role

In the explicit model, the symbol α12 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α12 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0012/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 13. Geometric Object Role

In the explicit model, the symbol P13 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P13 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0013/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 14. Geometric Object Role

In the explicit model, the symbol l14 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l14 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0014/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 15. Geometric Object Role

In the explicit model, the symbol α15 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α15 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0015/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 16. Geometric Object Role

In the explicit model, the symbol P16 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P16 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0016/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 17. Geometric Object Role

In the explicit model, the symbol l17 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l17 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0017/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 18. Geometric Object Role

In the explicit model, the symbol α18 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α18 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0018/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 19. Geometric Object Role

In the explicit model, the symbol P19 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P19 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0019/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 20. Geometric Object Role

In the explicit model, the symbol l20 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l20 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0020/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 21. Geometric Object Role

In the explicit model, the symbol α21 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α21 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0021/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 22. Geometric Object Role

In the explicit model, the symbol P22 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P22 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0022/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 23. Geometric Object Role

In the explicit model, the symbol l23 is designated as a line. What is its geometric role?

View answer and explanationLine

The prompt explicitly designates l23 as a line; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0023/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 24. Geometric Object Role

In the explicit model, the symbol α24 is designated as a plane. What is its geometric role?

View answer and explanationPlane

The prompt explicitly designates α24 as a plane; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0024/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 25. Geometric Object Role

In the explicit model, the symbol P25 is designated as a point. What is its geometric role?

View answer and explanationPoint

The prompt explicitly designates P25 as a point; the answer is not inferred from visual appearance.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-geometry-object-role-0025/)

Points, lines, and planes · qf-geometry-object-role · candidate





## 26. Explicit Incidence

Explicit incidence data: P1 lies on l1. Is P1 incident with l1?

View answer and explanationYes

According to the explicit incidence data, P1 lies on l1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0001/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 27. Explicit Incidence

Explicit incidence data: P2 does not lie on l2. Is P2 incident with l2?

View answer and explanationNo

According to the explicit incidence data, P2 does not lie on l2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0002/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 28. Explicit Incidence

Explicit incidence data: P3 lies on l3. Is P3 incident with l3?

View answer and explanationYes

According to the explicit incidence data, P3 lies on l3.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0003/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 29. Explicit Incidence

Explicit incidence data: P4 does not lie on l4. Is P4 incident with l4?

View answer and explanationNo

According to the explicit incidence data, P4 does not lie on l4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0004/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 30. Explicit Incidence

Explicit incidence data: P5 lies on l5. Is P5 incident with l5?

View answer and explanationYes

According to the explicit incidence data, P5 lies on l5.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0005/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 31. Explicit Incidence

Explicit incidence data: P6 does not lie on l6. Is P6 incident with l6?

View answer and explanationNo

According to the explicit incidence data, P6 does not lie on l6.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0006/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 32. Explicit Incidence

Explicit incidence data: P7 lies on l7. Is P7 incident with l7?

View answer and explanationYes

According to the explicit incidence data, P7 lies on l7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0007/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 33. Explicit Incidence

Explicit incidence data: P8 does not lie on l8. Is P8 incident with l8?

View answer and explanationNo

According to the explicit incidence data, P8 does not lie on l8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0008/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 34. Explicit Incidence

Explicit incidence data: P9 lies on l9. Is P9 incident with l9?

View answer and explanationYes

According to the explicit incidence data, P9 lies on l9.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0009/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 35. Explicit Incidence

Explicit incidence data: P10 does not lie on l10. Is P10 incident with l10?

View answer and explanationNo

According to the explicit incidence data, P10 does not lie on l10.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0010/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 36. Explicit Incidence

Explicit incidence data: P11 lies on l11. Is P11 incident with l11?

View answer and explanationYes

According to the explicit incidence data, P11 lies on l11.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0011/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 37. Explicit Incidence

Explicit incidence data: P12 does not lie on l12. Is P12 incident with l12?

View answer and explanationNo

According to the explicit incidence data, P12 does not lie on l12.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0012/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 38. Explicit Incidence

Explicit incidence data: P13 lies on l13. Is P13 incident with l13?

View answer and explanationYes

According to the explicit incidence data, P13 lies on l13.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0013/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 39. Explicit Incidence

Explicit incidence data: P14 does not lie on l14. Is P14 incident with l14?

View answer and explanationNo

According to the explicit incidence data, P14 does not lie on l14.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0014/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 40. Explicit Incidence

Explicit incidence data: P15 lies on l15. Is P15 incident with l15?

View answer and explanationYes

According to the explicit incidence data, P15 lies on l15.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0015/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 41. Explicit Incidence

Explicit incidence data: P16 does not lie on l16. Is P16 incident with l16?

View answer and explanationNo

According to the explicit incidence data, P16 does not lie on l16.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0016/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 42. Explicit Incidence

Explicit incidence data: P17 lies on l17. Is P17 incident with l17?

View answer and explanationYes

According to the explicit incidence data, P17 lies on l17.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0017/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 43. Explicit Incidence

Explicit incidence data: P18 does not lie on l18. Is P18 incident with l18?

View answer and explanationNo

According to the explicit incidence data, P18 does not lie on l18.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0018/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 44. Explicit Incidence

Explicit incidence data: P19 lies on l19. Is P19 incident with l19?

View answer and explanationYes

According to the explicit incidence data, P19 lies on l19.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0019/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 45. Explicit Incidence

Explicit incidence data: P20 does not lie on l20. Is P20 incident with l20?

View answer and explanationNo

According to the explicit incidence data, P20 does not lie on l20.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0020/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 46. Explicit Incidence

Explicit incidence data: P21 lies on l21. Is P21 incident with l21?

View answer and explanationYes

According to the explicit incidence data, P21 lies on l21.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0021/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 47. Explicit Incidence

Explicit incidence data: P22 does not lie on l22. Is P22 incident with l22?

View answer and explanationNo

According to the explicit incidence data, P22 does not lie on l22.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0022/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 48. Explicit Incidence

Explicit incidence data: P23 lies on l23. Is P23 incident with l23?

View answer and explanationYes

According to the explicit incidence data, P23 lies on l23.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0023/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 49. Explicit Incidence

Explicit incidence data: P24 does not lie on l24. Is P24 incident with l24?

View answer and explanationNo

According to the explicit incidence data, P24 does not lie on l24.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0024/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 50. Explicit Incidence

Explicit incidence data: P25 lies on l25. Is P25 incident with l25?

View answer and explanationYes

According to the explicit incidence data, P25 lies on l25.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-incidence-language-0025/)

Points, lines, and planes · qf-explicit-incidence-language · candidate





## 51. Explicit Collinearity

Explicit data: P1, Q1, R1 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0001/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 52. Explicit Collinearity

Explicit data: P2, Q2, R2 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0002/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 53. Explicit Collinearity

Explicit data: P3, Q3, R3 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0003/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 54. Explicit Collinearity

Explicit data: P4, Q4, R4 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0004/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 55. Explicit Collinearity

Explicit data: P5, Q5, R5 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0005/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 56. Explicit Collinearity

Explicit data: P6, Q6, R6 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0006/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 57. Explicit Collinearity

Explicit data: P7, Q7, R7 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0007/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 58. Explicit Collinearity

Explicit data: P8, Q8, R8 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0008/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 59. Explicit Collinearity

Explicit data: P9, Q9, R9 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0009/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 60. Explicit Collinearity

Explicit data: P10, Q10, R10 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0010/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 61. Explicit Collinearity

Explicit data: P11, Q11, R11 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0011/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 62. Explicit Collinearity

Explicit data: P12, Q12, R12 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0012/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 63. Explicit Collinearity

Explicit data: P13, Q13, R13 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0013/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 64. Explicit Collinearity

Explicit data: P14, Q14, R14 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0014/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 65. Explicit Collinearity

Explicit data: P15, Q15, R15 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0015/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 66. Explicit Collinearity

Explicit data: P16, Q16, R16 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0016/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 67. Explicit Collinearity

Explicit data: P17, Q17, R17 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0017/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 68. Explicit Collinearity

Explicit data: P18, Q18, R18 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0018/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 69. Explicit Collinearity

Explicit data: P19, Q19, R19 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0019/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 70. Explicit Collinearity

Explicit data: P20, Q20, R20 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0020/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 71. Explicit Collinearity

Explicit data: P21, Q21, R21 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0021/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 72. Explicit Collinearity

Explicit data: P22, Q22, R22 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0022/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 73. Explicit Collinearity

Explicit data: P23, Q23, R23 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0023/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 74. Explicit Collinearity

Explicit data: P24, Q24, R24 are not collinear. Are the three points collinear?

View answer and explanationNo

The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0024/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 75. Explicit Collinearity

Explicit data: P25, Q25, R25 are collinear. Are the three points collinear?

View answer and explanationYes

The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-collinearity-classification-0025/)

Points, lines, and planes · qf-explicit-collinearity-classification · candidate





## 76. Explicit Coplanarity

Explicit data: P1, Q1, R1, S1 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0001/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 77. Explicit Coplanarity

Explicit data: P2, Q2, R2, S2 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0002/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 78. Explicit Coplanarity

Explicit data: P3, Q3, R3, S3 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0003/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 79. Explicit Coplanarity

Explicit data: P4, Q4, R4, S4 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0004/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 80. Explicit Coplanarity

Explicit data: P5, Q5, R5, S5 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0005/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 81. Explicit Coplanarity

Explicit data: P6, Q6, R6, S6 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0006/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 82. Explicit Coplanarity

Explicit data: P7, Q7, R7, S7 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0007/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 83. Explicit Coplanarity

Explicit data: P8, Q8, R8, S8 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0008/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 84. Explicit Coplanarity

Explicit data: P9, Q9, R9, S9 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0009/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 85. Explicit Coplanarity

Explicit data: P10, Q10, R10, S10 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0010/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 86. Explicit Coplanarity

Explicit data: P11, Q11, R11, S11 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0011/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 87. Explicit Coplanarity

Explicit data: P12, Q12, R12, S12 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0012/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 88. Explicit Coplanarity

Explicit data: P13, Q13, R13, S13 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0013/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 89. Explicit Coplanarity

Explicit data: P14, Q14, R14, S14 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0014/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 90. Explicit Coplanarity

Explicit data: P15, Q15, R15, S15 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0015/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 91. Explicit Coplanarity

Explicit data: P16, Q16, R16, S16 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0016/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 92. Explicit Coplanarity

Explicit data: P17, Q17, R17, S17 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0017/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 93. Explicit Coplanarity

Explicit data: P18, Q18, R18, S18 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0018/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 94. Explicit Coplanarity

Explicit data: P19, Q19, R19, S19 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0019/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 95. Explicit Coplanarity

Explicit data: P20, Q20, R20, S20 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0020/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 96. Explicit Coplanarity

Explicit data: P21, Q21, R21, S21 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0021/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 97. Explicit Coplanarity

Explicit data: P22, Q22, R22, S22 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0022/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 98. Explicit Coplanarity

Explicit data: P23, Q23, R23, S23 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0023/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 99. Explicit Coplanarity

Explicit data: P24, Q24, R24, S24 are not coplanar. Are the four points coplanar?

View answer and explanationNo

The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0024/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate





## 100. Explicit Coplanarity

Explicit data: P25, Q25, R25, S25 are coplanar. Are the four points coplanar?

View answer and explanationYes

The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20260917-explicit-coplanarity-classification-0025/)

Points, lines, and planes · qf-explicit-coplanarity-classification · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20260917-point-line-plane/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20260917-point-line-plane.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20260917-point-line-plane/validation-report.json)