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Question 30770: Four Ordered Coordinate Columns, Axes, and Locations

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0060-30770 · q-20261011-advance-20261015-r07-coordinate-plane-0020

Original question and givens

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[7, 1], [1, 0], [0, 1], [-1, -19]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

  • G001 — Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[7, 1], [1, 0], [0, 1], [-1, -19]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-density15-coordinate-four-point-axis-masks, density15_coordinate_four_point_axis_masks, finite_ordered_coordinate_protocol]

After

derived = [[x_column, y_column, x_axis_mask, y_axis_mask, locations]]

Conditions: none

density14/15 use FULL-prefix underscores;density17 uses LOCAL hyphens.The coordinate and circle frames differ.Retain THIS family ordered answer roles/types and all original bilingual JSON/status.

Step identifiers and dependencies

Rule: R60_EXACT_perbank_operation_domain_FRAME_and_output_roles · Uses: G001

S002 · implies

Before

source roles = [0, 7, 1]

After

derived = [No, No, I]

Conditions: none

Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses.

Step identifiers and dependencies

Rule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S001

S003 · implies

Before

source roles = [1, 1, 0]

After

derived = [Yes, No, x axis]

Conditions: none

Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses.

Step identifiers and dependencies

Rule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S002

S004 · implies

Before

source roles = [2, 0, 1]

After

derived = [No, Yes, y axis]

Conditions: none

Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses.

Step identifiers and dependencies

Rule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S003

S005 · implies

Before

source roles = [3, -1, -19]

After

derived = [No, No, III]

Conditions: none

Check zero coordinates BEFORE quadrants.The origin lies on BOTH axes and in NO quadrant;axis points are not quadrant points.Keep all four positions and separate x/y columns without diagram guesses.

Step identifiers and dependencies

Rule: Coordinate_EACH_original_point_axes_BEFORE_quadrants · Uses: G001, S004

Reverse checks

  • S005 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
  • S004 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
  • S003 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
  • S002 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.
  • S001 · premise_and_result_audit — Reverse-check using the ORIGINAL data,types,indices and premises.Consistency auditing does not claim the conclusion uniquely determines its inputs.Keep finite candidates,independent review,formal proof and publication separate.

Result

([7, 1, 0, -1], [1, 0, 1, -19], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 5584ece9f94438b92d19855f820cefefad25f648d87cad3ec88f89b0babda681
  • candidate record SHA-256: 3120880551b6eed987564717ea3bfb74644668257fde178d0be6153129996aae
  • semantic review receipt SHA-256: d6b5a409bf933281a46617cd715d8016fd5ca3d6fb76f77d179ac2ecd9d608bf
  • question-first witness SHA-256: f80ecf598c6893a580af018e1a82849b33ee6887efb48a6a1d69569aa17f12e4
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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