# Ordered Coordinate Fields, Axes, and Equality

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-20261011-advance-20261015-r07-coordinate-plane-foundations · 2026-10-11 · 100 questions

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



## 1. Four Ordered Coordinate Columns, Axes, and Locations

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=[[0, 0], [1, 0], [0, -1], [-1, 1]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([0, 1, 0, -1], [0, 0, -1, 1], [Yes, Yes, No, No], [Yes, No, Yes, No], [origin, x-axis, y-axis, II])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([0, 1, 0, -1], [0, 0, -1, 1], [Yes, Yes, No, No], [Yes, No, Yes, No], [origin, x-axis, y-axis, II]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0001/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 2. Four Ordered Coordinate Columns, Axes, and Locations

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=[[1, 1], [-1, 1], [-1, -1], [1, -1]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([1, -1, -1, 1], [1, 1, -1, -1], [No, No, No, No], [No, No, No, No], [I, II, III, IV])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([1, -1, -1, 1], [1, 1, -1, -1], [No, No, No, No], [No, No, No, No], [I, II, III, IV]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0002/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 3. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-10, 1], [1, 0], [0, 1], [-1, -2]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-10, 1, 0, -1], [1, 0, 1, -2], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-10, 1, 0, -1], [1, 0, 1, -2], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0003/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 4. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-9, 1], [1, 0], [0, 1], [-1, -3]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-9, 1, 0, -1], [1, 0, 1, -3], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-9, 1, 0, -1], [1, 0, 1, -3], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0004/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 5. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-8, 1], [1, 0], [0, 1], [-1, -4]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-8, 1, 0, -1], [1, 0, 1, -4], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-8, 1, 0, -1], [1, 0, 1, -4], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0005/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 6. Four Ordered Coordinate Columns, Axes, and Locations

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, -5]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-7, 1, 0, -1], [1, 0, 1, -5], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-7, 1, 0, -1], [1, 0, 1, -5], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0006/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 7. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-6, 1], [1, 0], [0, 1], [-1, -6]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-6, 1, 0, -1], [1, 0, 1, -6], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-6, 1, 0, -1], [1, 0, 1, -6], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0007/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 8. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-5, 1], [1, 0], [0, 1], [-1, -7]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-5, 1, 0, -1], [1, 0, 1, -7], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-5, 1, 0, -1], [1, 0, 1, -7], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0008/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 9. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-4, 1], [1, 0], [0, 1], [-1, -8]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-4, 1, 0, -1], [1, 0, 1, -8], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-4, 1, 0, -1], [1, 0, 1, -8], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0009/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 10. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-3, 1], [1, 0], [0, 1], [-1, -9]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-3, 1, 0, -1], [1, 0, 1, -9], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-3, 1, 0, -1], [1, 0, 1, -9], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0010/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 11. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-2, 1], [1, 0], [0, 1], [-1, -10]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-2, 1, 0, -1], [1, 0, 1, -10], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-2, 1, 0, -1], [1, 0, 1, -10], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0011/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 12. Four Ordered Coordinate Columns, Axes, and Locations

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=[[-1, 1], [1, 0], [0, 1], [-1, -11]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([-1, 1, 0, -1], [1, 0, 1, -11], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-1, 1, 0, -1], [1, 0, 1, -11], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0012/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 13. Four Ordered Coordinate Columns, Axes, and Locations

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=[[0, 1], [1, 0], [0, 1], [-1, -12]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([0, 1, 0, -1], [1, 0, 1, -12], [No, Yes, No, No], [Yes, No, Yes, No], [y-axis, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([0, 1, 0, -1], [1, 0, 1, -12], [No, Yes, No, No], [Yes, No, Yes, No], [y-axis, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0013/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 14. Four Ordered Coordinate Columns, Axes, and Locations

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=[[1, 1], [1, 0], [0, 1], [-1, -13]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([1, 1, 0, -1], [1, 0, 1, -13], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([1, 1, 0, -1], [1, 0, 1, -13], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0014/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 15. Four Ordered Coordinate Columns, Axes, and Locations

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=[[2, 1], [1, 0], [0, 1], [-1, -14]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([2, 1, 0, -1], [1, 0, 1, -14], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([2, 1, 0, -1], [1, 0, 1, -14], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0015/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 16. Four Ordered Coordinate Columns, Axes, and Locations

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=[[3, 1], [1, 0], [0, 1], [-1, -15]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([3, 1, 0, -1], [1, 0, 1, -15], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([3, 1, 0, -1], [1, 0, 1, -15], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0016/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 17. Four Ordered Coordinate Columns, Axes, and Locations

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=[[4, 1], [1, 0], [0, 1], [-1, -16]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([4, 1, 0, -1], [1, 0, 1, -16], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([4, 1, 0, -1], [1, 0, 1, -16], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0017/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 18. Four Ordered Coordinate Columns, Axes, and Locations

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=[[5, 1], [1, 0], [0, 1], [-1, -17]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0018/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 19. Four Ordered Coordinate Columns, Axes, and Locations

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=[[6, 1], [1, 0], [0, 1], [-1, -18]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([6, 1, 0, -1], [1, 0, 1, -18], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([6, 1, 0, -1], [1, 0, 1, -18], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0019/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 20. Four Ordered Coordinate Columns, Axes, and Locations

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).

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

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([7, 1, 0, -1], [1, 0, 1, -19], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0020/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 21. Four Ordered Coordinate Columns, Axes, and Locations

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=[[8, 1], [1, 0], [0, 1], [-1, -20]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([8, 1, 0, -1], [1, 0, 1, -20], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([8, 1, 0, -1], [1, 0, 1, -20], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0021/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 22. Four Ordered Coordinate Columns, Axes, and Locations

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=[[9, 1], [1, 0], [0, 1], [-1, -21]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([9, 1, 0, -1], [1, 0, 1, -21], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([9, 1, 0, -1], [1, 0, 1, -21], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0022/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 23. Four Ordered Coordinate Columns, Axes, and Locations

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=[[10, 1], [1, 0], [0, 1], [-1, -22]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([10, 1, 0, -1], [1, 0, 1, -22], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([10, 1, 0, -1], [1, 0, 1, -22], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0023/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 24. Four Ordered Coordinate Columns, Axes, and Locations

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=[[11, 1], [1, 0], [0, 1], [-1, -23]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([11, 1, 0, -1], [1, 0, 1, -23], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([11, 1, 0, -1], [1, 0, 1, -23], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0024/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 25. Four Ordered Coordinate Columns, Axes, and Locations

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=[[12, 1], [1, 0], [0, 1], [-1, -24]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).

View answer and explanation([12, 1, 0, -1], [1, 0, 1, -24], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])

Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([12, 1, 0, -1], [1, 0, 1, -24], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0025/)

Coordinate plane · qf-density15-coordinate-four-point-axis-masks · candidate





## 26. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 0], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(0, 0, Yes)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (0, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0026/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 27. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], Q=[2, 1]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-1, 1, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-1, 1, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0027/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 28. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-10, 3], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-10, 3, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-10, 3, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0028/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 29. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-9, 4], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-9, 4, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-9, 4, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0029/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 30. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-8, 5], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-8, 5, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-8, 5, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0030/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 31. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-7, 6], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-7, 6, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-7, 6, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0031/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 32. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-6, 7], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-6, 7, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-6, 7, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0032/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 33. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-5, 8], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-5, 8, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-5, 8, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0033/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 34. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-4, 9], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-4, 9, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-4, 9, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0034/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 35. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-3, 10], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-3, 10, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-3, 10, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0035/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 36. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-2, 11], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-2, 11, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-2, 11, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0036/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 37. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(-1, 12, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-1, 12, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0037/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 38. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 13], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(0, 13, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (0, 13, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0038/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 39. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 14], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(1, 14, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (1, 14, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0039/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 40. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[2, 15], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(2, 15, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (2, 15, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0040/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 41. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[3, 16], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(3, 16, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (3, 16, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0041/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 42. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[4, 17], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(4, 17, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (4, 17, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0042/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 43. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[5, 18], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(5, 18, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (5, 18, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0043/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 44. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[6, 19], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(6, 19, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (6, 19, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0044/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 45. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[7, 20], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(7, 20, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (7, 20, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0045/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 46. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[8, 21], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(8, 21, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (8, 21, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0046/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 47. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[9, 22], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(9, 22, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (9, 22, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0047/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 48. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[10, 23], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(10, 23, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (10, 23, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0048/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 49. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[11, 24], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(11, 24, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (11, 24, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0049/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 50. Componentwise Coordinate Differences and Equality

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[12, 25], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.

View answer and explanation(12, 25, No)

Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (12, 25, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0050/)

Coordinate plane · qf-density15-coordinate-ordered-pair-compare · candidate





## 51. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 0], candidate=[0, 0], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([0, 0], [0, 0], Yes, Yes)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([0, 0], [0, 0], Yes, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0051/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 52. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 1], candidate=[1, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([1, 1], [0, 0], Yes, Yes)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([1, 1], [0, 0], Yes, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0052/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 53. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], candidate=[2, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([2, 1], [0, 0], Yes, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([2, 1], [0, 0], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0053/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 54. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], candidate=[1, 2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([2, 1], [-1, 1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([2, 1], [-1, 1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0054/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 55. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-8, 5], candidate=[6, -9], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([5, -8], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([5, -8], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0055/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 56. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-7, 6], candidate=[7, -8], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([6, -7], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([6, -7], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0056/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 57. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-6, 7], candidate=[8, -7], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([7, -6], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([7, -6], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0057/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 58. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-5, 8], candidate=[9, -6], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([8, -5], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([8, -5], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0058/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 59. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-4, 9], candidate=[10, -5], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([9, -4], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([9, -4], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0059/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 60. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-3, 10], candidate=[11, -4], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([10, -3], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([10, -3], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0060/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 61. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-2, 11], candidate=[12, -3], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([11, -2], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([11, -2], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0061/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 62. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], candidate=[13, -2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([12, -1], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([12, -1], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0062/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 63. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 13], candidate=[14, -1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([13, 0], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([13, 0], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0063/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 64. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 14], candidate=[15, 0], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([14, 1], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([14, 1], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0064/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 65. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[2, 15], candidate=[16, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([15, 2], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([15, 2], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0065/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 66. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[3, 16], candidate=[17, 2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([16, 3], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([16, 3], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0066/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 67. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[4, 17], candidate=[18, 3], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([17, 4], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([17, 4], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0067/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 68. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[5, 18], candidate=[19, 4], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([18, 5], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([18, 5], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0068/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 69. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[6, 19], candidate=[20, 5], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([19, 6], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([19, 6], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0069/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 70. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[7, 20], candidate=[21, 6], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([20, 7], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([20, 7], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0070/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 71. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[8, 21], candidate=[22, 7], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([21, 8], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([21, 8], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0071/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 72. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[9, 22], candidate=[23, 8], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([22, 9], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([22, 9], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0072/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 73. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[10, 23], candidate=[24, 9], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([23, 10], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([23, 10], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0073/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 74. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[11, 24], candidate=[25, 10], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([24, 11], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([24, 11], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0074/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 75. Coordinate-Field Swap Candidate Audit

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[12, 25], candidate=[26, 11], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).

View answer and explanation([25, 12], [1, -1], No, No)

Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([25, 12], [1, -1], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0075/)

Coordinate plane · qf-density15-coordinate-swap-candidate-audit · candidate





## 76. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[0, 0], [0, 0], [0, 0]], [Yes, Yes, Yes], none)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, 0], [0, 0]], [Yes, Yes, Yes], none).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0076/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 77. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[1, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[1, 0], [0, 0], [0, 0]], [No, Yes, Yes], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[1, 0], [0, 0], [0, 0]], [No, Yes, Yes], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0077/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 78. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, -1], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[0, 0], [0, -1], [0, 0]], [Yes, No, Yes], 1)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, -1], [0, 0]], [Yes, No, Yes], 1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0078/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 79. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[1, 1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[0, 0], [0, 0], [1, 1]], [Yes, Yes, No], 2)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, 0], [1, 1]], [Yes, Yes, No], 2).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0079/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 80. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-8, 1], [0, 0]], [[0, 4], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-8, 1], [0, 4], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-8, 1], [0, 4], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0080/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 81. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-7, 1], [0, 0]], [[0, 5], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-7, 1], [0, 5], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-7, 1], [0, 5], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0081/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 82. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-6, 1], [0, 0]], [[0, 6], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-6, 1], [0, 6], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-6, 1], [0, 6], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0082/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 83. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-5, 1], [0, 0]], [[0, 7], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-5, 1], [0, 7], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-5, 1], [0, 7], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0083/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 84. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-4, 1], [0, 0]], [[0, 8], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-4, 1], [0, 8], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-4, 1], [0, 8], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0084/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 85. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-3, 1], [0, 0]], [[0, 9], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-3, 1], [0, 9], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-3, 1], [0, 9], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0085/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 86. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-2, 1], [0, 0]], [[0, 10], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-2, 1], [0, 10], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-2, 1], [0, 10], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0086/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 87. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-1, 1], [0, 0]], [[0, 11], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[-1, 1], [0, 11], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-1, 1], [0, 11], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0087/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 88. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 1], [0, 0]], [[0, 12], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[0, 1], [0, 12], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 1], [0, 12], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0088/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 89. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[1, 1], [0, 0]], [[0, 13], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[1, 1], [0, 13], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[1, 1], [0, 13], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0089/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 90. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[2, 1], [0, 0]], [[0, 14], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[2, 1], [0, 14], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[2, 1], [0, 14], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0090/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 91. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[3, 1], [0, 0]], [[0, 15], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[3, 1], [0, 15], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[3, 1], [0, 15], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0091/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 92. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[4, 1], [0, 0]], [[0, 16], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[4, 1], [0, 16], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[4, 1], [0, 16], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0092/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 93. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[5, 1], [0, 0]], [[0, 17], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[5, 1], [0, 17], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[5, 1], [0, 17], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0093/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 94. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[6, 1], [0, 0]], [[0, 18], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[6, 1], [0, 18], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[6, 1], [0, 18], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0094/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 95. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[7, 1], [0, 0]], [[0, 19], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[7, 1], [0, 19], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[7, 1], [0, 19], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0095/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 96. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[8, 1], [0, 0]], [[0, 20], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[8, 1], [0, 20], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[8, 1], [0, 20], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0096/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 97. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[9, 1], [0, 0]], [[0, 21], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[9, 1], [0, 21], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[9, 1], [0, 21], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0097/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 98. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[10, 1], [0, 0]], [[0, 22], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[10, 1], [0, 22], [0, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[10, 1], [0, 22], [0, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0098/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 99. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[11, 1], [0, 0]], [[0, 23], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[11, 1], [0, 23], [1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[11, 1], [0, 23], [1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0099/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate





## 100. Three Ordered Coordinate Comparisons and First Mismatch

Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[12, 1], [0, 0]], [[0, 24], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).

View answer and explanation([[12, 1], [0, 24], [-1, -1]], [No, No, No], 0)

Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[12, 1], [0, 24], [-1, -1]], [No, No, No], 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261011-advance-20261015-r07-coordinate-plane-0100/)

Coordinate plane · qf-density15-coordinate-first-mismatch-index · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261011-advance-20261015-r07-coordinate-plane-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261011-advance-20261015-r07-coordinate-plane-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261011-advance-20261015-r07-coordinate-plane-foundations/validation-report.json)