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-20260930-r07-coordinate-plane-foundations · 2026-09-30 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
In one explicit Cartesian coordinate system, classify P=(-2,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant III
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-2,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant III
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-2,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
x-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-2,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant II
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-2,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant II
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-1,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant III
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-1,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant III
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant III; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-1,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
x-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-1,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant II
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(-1,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant II
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant II; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(0,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
y-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(0,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
y-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(0,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
origin
Check which coordinates are zero and the signs of the nonzero coordinates. P is at origin; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(0,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
y-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(0,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
y-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at y-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(1,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant IV
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(1,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant IV
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(1,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
x-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(1,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant I
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(1,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant I
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(2,-2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant IV
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(2,-1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant IV
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant IV; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(2,0) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
x-axis
Check which coordinates are zero and the signs of the nonzero coordinates. P is at x-axis; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(2,1) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant I
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, classify P=(2,2) as a quadrant, an axis point, or the origin. Axis points are not in quadrants.
quadrant I
Check which coordinates are zero and the signs of the nonzero coordinates. P is at quadrant I; the origin lies on both axes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-location · candidate
In one explicit Cartesian coordinate system, is P=(-2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-2,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-2,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.
Yes
The x-axis condition is y=0. Componentwise checking gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-2,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-2,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-1,-2) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-1,-1) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-1,0) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-1,1) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(-1,2) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(0,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(0,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
Yes
The y-axis condition is x=0. Componentwise checking gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(0,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.
Yes
The x-axis condition is y=0. Componentwise checking gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(0,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
Yes
The y-axis condition is x=0. Componentwise checking gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(0,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(1,-2) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(1,-1) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(1,0) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(1,1) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(1,2) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(2,-2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(2,-1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(2,0) on the x-axis? Answer Yes or No; the origin belongs to both axes.
Yes
The x-axis condition is y=0. Componentwise checking gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(2,1) on the y-axis? Answer Yes or No; the origin belongs to both axes.
No
The y-axis condition is x=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, is P=(2,2) on the x-axis? Answer Yes or No; the origin belongs to both axes.
No
The x-axis condition is y=0. Componentwise checking gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-axis-membership · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,-2)? Read the ordered pair as (x,y).
-2
The first component is -2, so the x-coordinate is -2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-2,-1)? Read the ordered pair as (x,y).
-1
The second component is -1, so the y-coordinate is -1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,0)? Read the ordered pair as (x,y).
-2
The first component is -2, so the x-coordinate is -2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-2,1)? Read the ordered pair as (x,y).
1
The second component is 1, so the y-coordinate is 1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-2,2)? Read the ordered pair as (x,y).
-2
The first component is -2, so the x-coordinate is -2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,-2)? Read the ordered pair as (x,y).
-2
The second component is -2, so the y-coordinate is -2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-1,-1)? Read the ordered pair as (x,y).
-1
The first component is -1, so the x-coordinate is -1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,0)? Read the ordered pair as (x,y).
0
The second component is 0, so the y-coordinate is 0.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(-1,1)? Read the ordered pair as (x,y).
-1
The first component is -1, so the x-coordinate is -1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(-1,2)? Read the ordered pair as (x,y).
2
The second component is 2, so the y-coordinate is 2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,-2)? Read the ordered pair as (x,y).
0
The first component is 0, so the x-coordinate is 0.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(0,-1)? Read the ordered pair as (x,y).
-1
The second component is -1, so the y-coordinate is -1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,0)? Read the ordered pair as (x,y).
0
The first component is 0, so the x-coordinate is 0.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(0,1)? Read the ordered pair as (x,y).
1
The second component is 1, so the y-coordinate is 1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(0,2)? Read the ordered pair as (x,y).
0
The first component is 0, so the x-coordinate is 0.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,-2)? Read the ordered pair as (x,y).
-2
The second component is -2, so the y-coordinate is -2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(1,-1)? Read the ordered pair as (x,y).
1
The first component is 1, so the x-coordinate is 1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,0)? Read the ordered pair as (x,y).
0
The second component is 0, so the y-coordinate is 0.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(1,1)? Read the ordered pair as (x,y).
1
The first component is 1, so the x-coordinate is 1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(1,2)? Read the ordered pair as (x,y).
2
The second component is 2, so the y-coordinate is 2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,-2)? Read the ordered pair as (x,y).
2
The first component is 2, so the x-coordinate is 2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(2,-1)? Read the ordered pair as (x,y).
-1
The second component is -1, so the y-coordinate is -1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,0)? Read the ordered pair as (x,y).
2
The first component is 2, so the x-coordinate is 2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the y-coordinate of P=(2,1)? Read the ordered pair as (x,y).
1
The second component is 1, so the y-coordinate is 1.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In one explicit Cartesian coordinate system, what is the x-coordinate of P=(2,2)? Read the ordered pair as (x,y).
2
The first component is 2, so the x-coordinate is 2.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-component · candidate
In the same explicit Cartesian coordinate system, are P=(-2,-2) and Q=(-2,-2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-2,-1) and Q=(-1,-1) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-2,0) and Q=(-2,0) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-2,1) and Q=(-2,2) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-2,2) and Q=(-2,2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-1,-2) and Q=(0,-2) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-1,-1) and Q=(-1,-1) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-1,0) and Q=(0,0) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-1,1) and Q=(-1,1) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(-1,2) and Q=(-1,3) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(0,-2) and Q=(0,-2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(0,-1) and Q=(1,-1) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(0,0) and Q=(0,0) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(0,1) and Q=(1,1) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(0,2) and Q=(0,2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(1,-2) and Q=(1,-1) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(1,-1) and Q=(1,-1) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(1,0) and Q=(2,0) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(1,1) and Q=(1,1) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(1,2) and Q=(2,2) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(2,-2) and Q=(2,-2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(2,-1) and Q=(2,0) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(2,0) and Q=(2,0) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(2,1) and Q=(3,1) the same point? Compare corresponding coordinates.
No
Point equality requires equality of both corresponding components. The componentwise comparison gives No.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
In the same explicit Cartesian coordinate system, are P=(2,2) and Q=(2,2) the same point? Compare corresponding coordinates.
Yes
Point equality requires equality of both corresponding components. The componentwise comparison gives Yes.
Reviewed step-by-step derivation
Coordinate plane · qf-coordinate-point-equality · candidate
Canonical question JSONL · English JSONL · Validation report