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.
In the explicit model, the symbol P1 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P1 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l2 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l2 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α3 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α3 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P4 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P4 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l5 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l5 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α6 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α6 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P7 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P7 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l8 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l8 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α9 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α9 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P10 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P10 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l11 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l11 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α12 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α12 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P13 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P13 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l14 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l14 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α15 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α15 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P16 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P16 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l17 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l17 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α18 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α18 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P19 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P19 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l20 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l20 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α21 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α21 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P22 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P22 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol l23 is designated as a line. What is its geometric role?
Line
The prompt explicitly designates l23 as a line; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol α24 is designated as a plane. What is its geometric role?
Plane
The prompt explicitly designates α24 as a plane; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
In the explicit model, the symbol P25 is designated as a point. What is its geometric role?
Point
The prompt explicitly designates P25 as a point; the answer is not inferred from visual appearance.
Reviewed step-by-step derivation
Points, lines, and planes · qf-geometry-object-role · candidate
Explicit incidence data: P1 lies on l1. Is P1 incident with l1?
Yes
According to the explicit incidence data, P1 lies on l1.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P2 does not lie on l2. Is P2 incident with l2?
No
According to the explicit incidence data, P2 does not lie on l2.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P3 lies on l3. Is P3 incident with l3?
Yes
According to the explicit incidence data, P3 lies on l3.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P4 does not lie on l4. Is P4 incident with l4?
No
According to the explicit incidence data, P4 does not lie on l4.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P5 lies on l5. Is P5 incident with l5?
Yes
According to the explicit incidence data, P5 lies on l5.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P6 does not lie on l6. Is P6 incident with l6?
No
According to the explicit incidence data, P6 does not lie on l6.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P7 lies on l7. Is P7 incident with l7?
Yes
According to the explicit incidence data, P7 lies on l7.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P8 does not lie on l8. Is P8 incident with l8?
No
According to the explicit incidence data, P8 does not lie on l8.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P9 lies on l9. Is P9 incident with l9?
Yes
According to the explicit incidence data, P9 lies on l9.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P10 does not lie on l10. Is P10 incident with l10?
No
According to the explicit incidence data, P10 does not lie on l10.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P11 lies on l11. Is P11 incident with l11?
Yes
According to the explicit incidence data, P11 lies on l11.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P12 does not lie on l12. Is P12 incident with l12?
No
According to the explicit incidence data, P12 does not lie on l12.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P13 lies on l13. Is P13 incident with l13?
Yes
According to the explicit incidence data, P13 lies on l13.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P14 does not lie on l14. Is P14 incident with l14?
No
According to the explicit incidence data, P14 does not lie on l14.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P15 lies on l15. Is P15 incident with l15?
Yes
According to the explicit incidence data, P15 lies on l15.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P16 does not lie on l16. Is P16 incident with l16?
No
According to the explicit incidence data, P16 does not lie on l16.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P17 lies on l17. Is P17 incident with l17?
Yes
According to the explicit incidence data, P17 lies on l17.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P18 does not lie on l18. Is P18 incident with l18?
No
According to the explicit incidence data, P18 does not lie on l18.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P19 lies on l19. Is P19 incident with l19?
Yes
According to the explicit incidence data, P19 lies on l19.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P20 does not lie on l20. Is P20 incident with l20?
No
According to the explicit incidence data, P20 does not lie on l20.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P21 lies on l21. Is P21 incident with l21?
Yes
According to the explicit incidence data, P21 lies on l21.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P22 does not lie on l22. Is P22 incident with l22?
No
According to the explicit incidence data, P22 does not lie on l22.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P23 lies on l23. Is P23 incident with l23?
Yes
According to the explicit incidence data, P23 lies on l23.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P24 does not lie on l24. Is P24 incident with l24?
No
According to the explicit incidence data, P24 does not lie on l24.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit incidence data: P25 lies on l25. Is P25 incident with l25?
Yes
According to the explicit incidence data, P25 lies on l25.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-incidence-language · candidate
Explicit data: P1, Q1, R1 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P2, Q2, R2 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P3, Q3, R3 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P4, Q4, R4 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P5, Q5, R5 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P6, Q6, R6 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P7, Q7, R7 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P8, Q8, R8 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P9, Q9, R9 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P10, Q10, R10 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P11, Q11, R11 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P12, Q12, R12 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P13, Q13, R13 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P14, Q14, R14 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P15, Q15, R15 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P16, Q16, R16 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P17, Q17, R17 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P18, Q18, R18 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P19, Q19, R19 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P20, Q20, R20 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P21, Q21, R21 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P22, Q22, R22 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P23, Q23, R23 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P24, Q24, R24 are not collinear. Are the three points collinear?
No
The prompt explicitly states that the points are not collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P25, Q25, R25 are collinear. Are the three points collinear?
Yes
The prompt explicitly states that the points are collinear; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-collinearity-classification · candidate
Explicit data: P1, Q1, R1, S1 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P2, Q2, R2, S2 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P3, Q3, R3, S3 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P4, Q4, R4, S4 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P5, Q5, R5, S5 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P6, Q6, R6, S6 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P7, Q7, R7, S7 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P8, Q8, R8, S8 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P9, Q9, R9, S9 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P10, Q10, R10, S10 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P11, Q11, R11, S11 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P12, Q12, R12, S12 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P13, Q13, R13, S13 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P14, Q14, R14, S14 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P15, Q15, R15, S15 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P16, Q16, R16, S16 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P17, Q17, R17, S17 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P18, Q18, R18, S18 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P19, Q19, R19, S19 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P20, Q20, R20, S20 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P21, Q21, R21, S21 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P22, Q22, R22, S22 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P23, Q23, R23, S23 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P24, Q24, R24, S24 are not coplanar. Are the four points coplanar?
No
The prompt explicitly states that the points are not coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Explicit data: P25, Q25, R25, S25 are coplanar. Are the four points coplanar?
Yes
The prompt explicitly states that the points are coplanar; no conclusion is inferred from a drawing.
Reviewed step-by-step derivation
Points, lines, and planes · qf-explicit-coplanarity-classification · candidate
Canonical question JSONL · English JSONL · Validation report