Grade 6 Math Practice Test: The Coordinate Plane in All Four Quadrants
- The Coordinate Plane in All Four Quadrants
- 10 questions
- 12 minutes
This test covers plotting points with negative coordinates, the four quadrants, reflections across the x-axis and y-axis, and distances between points that share a coordinate. Tip: the first number tells you left or right, the second tells you up or down.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
In which quadrant is the point (−3, 5)?
Correct answer: B
A negative x-coordinate means left of the y-axis, and a positive y-coordinate means above the x-axis. Left and up is Quadrant II.
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Question 2
The point (4, −2) is reflected across the x-axis. Where is the new point?
Correct answer: C
A reflection across the x-axis keeps the x-coordinate and changes the sign of the y-coordinate: (4, −2) becomes (4, 2). (−4, −2) is a reflection across the y-axis.
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Question 3
The point (−6, −1) is reflected across the y-axis. Where is the new point?
Correct answer: A
A reflection across the y-axis changes the sign of the x-coordinate and keeps the y-coordinate: (−6, −1) becomes (6, −1). (−6, 1) is a reflection across the x-axis.
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Question 4
How many units apart are the points (−3, 4) and (5, 4)?
Correct answer: D
The points have the same y-coordinate, so count along the x-axis: 3 units from −3 to 0 and 5 more to 5, so |−3| + |5| = 8 units. 2 subtracts 3 from 5.
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Question 5
How many units apart are the points (2, −6) and (2, 3)?
Correct answer: D
The points have the same x-coordinate, so count along the y-axis: 6 units from −6 to 0 and 3 more to 3, so |−6| + |3| = 9 units. 3 subtracts 3 from 6.
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Question 6
Point P is 5 units to the left of the y-axis and 2 units below the x-axis. What are its coordinates?
Correct answer: B
Left of the y-axis gives a negative x-coordinate, −5, and below the x-axis gives a negative y-coordinate, −2. (−2, −5) writes the coordinates in the wrong order.
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Question 7
A rectangle has vertices at (−2, 3), (4, 3), (4, −1) and (−2, −1). What is its perimeter?
Correct answer: A
The width is |−2| + |4| = 6 units and the height is |3| + |−1| = 4 units. Perimeter = 2 × 6 + 2 × 4 = 20 units. 24 is the area, not the perimeter.
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Question 8
Three vertices of a square are (−1, 2), (3, 2) and (3, −2). What is the fourth vertex?
Correct answer: A
The fourth vertex must be directly below (−1, 2) and level with (3, −2), so it shares the x-coordinate −1 and the y-coordinate −2. All four sides are then 4 units long.
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Question 9
Which point is on the y-axis, below the origin?
Correct answer: C
Points on the y-axis have an x-coordinate of 0, and a negative y-coordinate puts the point below the origin, so (0, −4). (−4, 0) is on the x-axis.
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Question 10
On a town map, each unit is one block. The library is at (−4, 1) and the school is at (−4, −6).
How many blocks apart are they?
Correct answer: B
The x-coordinates match, so the distance is |1| + |−6| = 1 + 6 = 7 blocks. 5 comes from subtracting 1 from 6, which works only when both points are on the same side of the x-axis.
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