Middle School Math Quiz: Understand Signs In Coordinate Plane
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Understand Signs In Coordinate PlaneQuestion 1 of 20

Point PP is located at (−4,7)(-4, 7) and point QQ is located at (4,−7)(4, -7). If you reflect point PP across the xx-axis and then across the yy-axis, what is the relationship between the final position and point QQ?

They are the same point with identical coordinates
They are different points separated by 14 units horizontally
They are different points separated by 14 units vertically
They are different points separated by 14 units diagonally
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Middle School Math Quiz

Middle School Math Quiz: Understand Signs In Coordinate Plane

Practice Understand Signs In Coordinate Plane in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Understand Signs In Coordinate Plane, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

Point PP is located at (−4,7)(-4, 7) and point QQ is located at (4,−7)(4, -7). If you reflect point PP across the xx-axis and then across the yy-axis, what is the relationship between the final position and point QQ?

  1. They are the same point with identical coordinates (correct answer)
  2. They are different points separated by 14 units horizontally
  3. They are different points separated by 14 units vertically
  4. They are different points separated by 14 units diagonally
Explanation: Reflecting P(−4,7)P(-4, 7) across the xx-axis gives (−4,−7)(-4, -7). Then reflecting across the yy-axis gives (4,−7)(4, -7), which is exactly point QQ. When two points differ only by signs in both coordinates, reflecting across both axes maps one to the other. Choice B is wrong because the points are identical after the reflections. Choice C is wrong because there's no vertical separation. Choice D is wrong because the final positions coincide.

Question 2

Two points are A(3,5)A(3,5) and E(−3,5)E(-3,5). How are these points related on the coordinate plane?

  1. They are reflections across the origin.
  2. They are reflections across the yy-axis. (correct answer)
  3. They are not related by any reflection.
  4. They are reflections across the xx-axis.
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). Points A(3,5) and E(-3,5) differ only in x-sign, so they are reflections across the y-axis, which is choice B. A common error is thinking they are across x-axis when y-signs are the same, or claiming no reflection. Reflections: identify which sign differs (only x for y-axis), understand symmetry as mirror image across axis. Mistakes include claiming origin reflection when only one sign differs or confusing the axes.

Question 3

The point A(3,5)A(3,5) is reflected across the yy-axis. What is the coordinate of the reflected point?

  1. (−3,−5)(-3,-5)
  2. (−3,5)(-3,5) (correct answer)
  3. (5,3)(5,3)
  4. (3,−5)(3,-5)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location, with Quadrant I for (+,+), II for (-,+), III for (-,-), and IV for (+,-), and points differing only by signs are reflections across axes. Quadrants are defined as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate for left/right of y-axis (positive right, negative left) and y-coordinate for above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs, like (3,5) and (-3,5) across y-axis (x-sign flip), (3,5) and (3,-5) across x-axis (y-sign flip), or (3,5) and (-3,-5) across origin (both flips). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) to (-3,5) across y-axis, (3,-5) across x-axis, (-3,-5) across origin. Reflecting A(3,5) across the y-axis flips the x-sign to (-3,5). A common error is flipping the wrong coordinate, like changing y instead of x for y-axis reflection. Reflections: identify which sign(s) differ (only x→y-axis reflection, only y→x-axis reflection, both→origin reflection), understand symmetry (reflection creates mirror image across axis). Avoid mistakes like reflection changes wrong coordinate, or claiming no relationship when signs differ.

Question 4

A map of a classroom floor uses a coordinate plane. The teacher marks the point B(−4,2)B(-4,2). Which statement correctly describes where BB is located?

Remember: a negative xx means left of the yy-axis, and a positive yy means above the xx-axis.

  1. Left of the yy-axis and above the xx-axis (Quadrant II) (correct answer)
  2. Left of the yy-axis and below the xx-axis (Quadrant III)
  3. Right of the yy-axis and above the xx-axis (Quadrant I)
  4. Right of the yy-axis and below the xx-axis (Quadrant IV)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). For point B(-4,2), x is negative (left of y-axis) and y is positive (above x-axis), placing it in Quadrant II, which matches choice A describing left and above. A common error is mixing up left/right with quadrants, like thinking negative x and positive y is Quadrant III instead of II. To determine the quadrant: (1) check x-sign (negative means left side, quadrants II or III), (2) check y-sign (positive means upper, quadrants I or II), (3) combine to x negative y positive for II. Mistakes often include confusing II and IV, or claiming signs don't determine position relative to axes.

Question 5

A student plots (3,5)(3,5) on a coordinate plane. What is the reflection of (3,5)(3,5) across the xx-axis?​

  1. (−3,5)(-3,5)
  2. (−3,−5)(-3,-5)
  3. (3,−5)(3,-5) (correct answer)
  4. (5,3)(5,3)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are divided as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate that the x-coordinate sign shows left/right of y-axis (x positive→right, x negative→left), y-coordinate sign shows above/below x-axis (y positive→above, y negative→below); reflections occur when ordered pairs differ only in signs—(3,5) and (-3,5) differ in x-sign only (reflected across y-axis), (3,5) and (3,-5) differ in y-sign (reflected across x-axis), (3,5) and (-3,-5) differ in both (reflected across origin through both axes). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive→Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above)→Quadrant II; reflections: (3,5) across y-axis flips x-sign: (-3,5), across x-axis flips y-sign: (3,-5), across origin flips both: (-3,-5). The reflection of (3,5) across the x-axis is (3,-5). A common error is flipping the x-sign instead for x-axis reflection, or choosing the origin reflection by flipping both. Reflections: identify which sign(s) differ (only x→y-axis reflection, only y→x-axis reflection, both→origin reflection), understand symmetry (reflection creates mirror image across axis). Quadrant order is counterclockwise from upper right (I→II→III→IV), and mistakes include reflection changes wrong coordinate, like flipping x for x-axis.

Question 6

Point A(3,5)A(3,5) is reflected across the xx-axis. What are the coordinates of the reflected point?

  1. (−3,5)(-3,5)
  2. (3,−5)(3,-5) (correct answer)
  3. (5,3)(5,3)
  4. (−3,−5)(-3,-5)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). Reflecting A(3,5) across the x-axis flips the y-sign to (3,-5), which is choice B. A common error is flipping the x-sign for x-axis reflection, thinking it changes x when it should change y. Reflections: identify which sign differs (only y for x-axis), understand symmetry as mirror image across axis. Mistakes include reflection changing the wrong coordinate or confusing x-axis with y-axis reflection.

Question 7

Point A(3,5)A(3,5) is reflected across the origin. What are the coordinates of the reflected point?

  1. (−3,5)(-3,5)
  2. (3,5)(3,5)
  3. (−3,−5)(-3,-5) (correct answer)
  4. (3,−5)(3,-5)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). Reflecting A(3,5) across the origin flips both signs to (-3,-5), which is choice C. A common error is flipping only one sign for origin reflection, or claiming it's across x-axis instead. Reflections: identify which signs differ (both for origin), understand symmetry as mirror image through both axes. Mistakes include claiming no relationship when both signs differ or confusing origin with single-axis reflections.

Question 8

In a video game map, a treasure is at (−3,−5)(-3,-5). In which quadrant is (−3,−5)(-3,-5) located?​

  1. Quadrant III (correct answer)
  2. Quadrant II
  3. Quadrant IV
  4. Quadrant I
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are divided as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate that the x-coordinate sign shows left/right of y-axis (x positive→right, x negative→left), y-coordinate sign shows above/below x-axis (y positive→above, y negative→below); reflections occur when ordered pairs differ only in signs—(3,5) and (-3,5) differ in x-sign only (reflected across y-axis), (3,5) and (3,-5) differ in y-sign (reflected across x-axis), (3,5) and (-3,-5) differ in both (reflected across origin through both axes). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive→Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above)→Quadrant II; reflections: (3,5) across y-axis flips x-sign: (-3,5), across x-axis flips y-sign: (3,-5), across origin flips both: (-3,-5). The point (-3,-5) is in Quadrant III because both coordinates are negative. A common error is identifying (-,-) as Quadrant II instead of III, or confusing quadrant numbering like thinking III is upper left. To determine the quadrant: (1) check x-coordinate sign (positive→right side quadrants I or IV, negative→left side II or III), (2) check y-coordinate sign (positive→upper quadrants I or II, negative→lower III or IV), (3) combine (both positive→I, x neg y pos→II, both neg→III, x pos y neg→IV). Quadrant order is counterclockwise from upper right (I→II→III→IV), and mistakes often include quadrant identification wrong, especially confusing III and IV.

Question 9

On a coordinate plane, the drama club marks a prop location at (3,5)(3,5). In which quadrant is (3,5)(3,5) located?​

  1. Quadrant IV
  2. Quadrant II
  3. Quadrant I (correct answer)
  4. Quadrant III
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are divided as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate that the x-coordinate sign shows left/right of y-axis (x positive→right, x negative→left), y-coordinate sign shows above/below x-axis (y positive→above, y negative→below); reflections occur when ordered pairs differ only in signs—(3,5) and (-3,5) differ in x-sign only (reflected across y-axis), (3,5) and (3,-5) differ in y-sign (reflected across x-axis), (3,5) and (-3,-5) differ in both (reflected across origin through both axes). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive→Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above)→Quadrant II; reflections: (3,5) across y-axis flips x-sign: (-3,5), across x-axis flips y-sign: (3,-5), across origin flips both: (-3,-5). The point (3,5) is in Quadrant I because both coordinates are positive. A common error is identifying (+,+) as Quadrant IV instead of I, or confusing quadrant numbering like thinking I is lower right. To determine the quadrant: (1) check x-coordinate sign (positive→right side quadrants I or IV, negative→left side II or III), (2) check y-coordinate sign (positive→upper quadrants I or II, negative→lower III or IV), (3) combine (both positive→I, x neg y pos→II, both neg→III, x pos y neg→IV). Quadrant order is counterclockwise from upper right (I→II→III→IV), and mistakes often include quadrant identification wrong, especially confusing I and IV.

Question 10

The coordinate plane shows points JJ, KK, and LL. Which statement correctly describes a reflection relationship between two of these points?

  1. Points JJ and KK are reflections across the yy-axis because they have the same yy-coordinate
  2. Points JJ and LL are reflections across the xx-axis because they have opposite yy-coordinates
  3. Points KK and LL are reflections across both axes because all their coordinates have opposite signs (correct answer)
  4. Points JJ and KK are reflections across the xx-axis because they have different xx-coordinates
Explanation: Point JJ is at (2,5)(2, 5), point KK is at (−2,5)(-2, 5), and point LL is at (2,−5)(2, -5). Points K(−2,5)K(-2, 5) and L(2,−5)L(2, -5) differ in the signs of both coordinates, making them reflections across both axes. Choice A is wrong because JJ and KK are reflections across the yy-axis, but the reason given is incomplete. Choice B is wrong because JJ and LL have the same xx-coordinate, making them reflections across the xx-axis, not because of opposite yy-coordinates alone. Choice D is wrong because having different xx-coordinates doesn't determine the type of reflection.

Question 11

The point A(3,5)A(3,5) is reflected across the xx-axis. What is the coordinate of the reflected point?

  1. (5,3)(5,3)
  2. (−3,−5)(-3,-5)
  3. (3,−5)(3,-5) (correct answer)
  4. (−3,5)(-3,5)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location, with Quadrant I for (+,+), II for (-,+), III for (-,-), and IV for (+,-), and points differing only by signs are reflections across axes. Quadrants are defined as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate for left/right of y-axis (positive right, negative left) and y-coordinate for above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs, like (3,5) and (-3,5) across y-axis (x-sign flip), (3,5) and (3,-5) across x-axis (y-sign flip), or (3,5) and (-3,-5) across origin (both flips). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) to (-3,5) across y-axis, (3,-5) across x-axis, (-3,-5) across origin. Reflecting A(3,5) across the x-axis flips the y-sign to (3,-5). A common error is flipping the x-sign instead, like for y-axis reflection when it's x-axis. Reflections: identify which sign(s) differ (only x→y-axis reflection, only y→x-axis reflection, both→origin reflection), understand symmetry (reflection creates mirror image across axis). Avoid mistakes like reflection changes wrong coordinate, or confusing x-axis with y-axis flips.

Question 12

In the coordinate plane shown, point MM is reflected across the yy-axis to create point NN. If point NN is then reflected across the xx-axis to create point PP, in which quadrant will point PP be located?

  1. Quadrant I, because both coordinates become positive after the reflections
  2. Quadrant II, because the xx-coordinate changes sign twice but yy-coordinate changes once
  3. Quadrant III, because both coordinates change sign an odd number of times
  4. Quadrant IV, because the xx-coordinate returns to positive and yy-coordinate becomes negative (correct answer)
Explanation: Point MM is at (−6,2)(-6, 2) in Quadrant II. Reflecting across the yy-axis gives N(6,2)N(6, 2) in Quadrant I. Reflecting NN across the xx-axis gives P(6,−2)P(6, -2) in Quadrant IV. The xx-coordinate changes from negative to positive (one sign change), and the yy-coordinate changes from positive to negative (one sign change). Choice A is wrong because the yy-coordinate becomes negative. Choice B is wrong because xx changes sign only once. Choice C is wrong because the final xx-coordinate is positive.

Question 13

Points A(3,5)A(3,5) and E(−3,5)E(-3,5) are plotted on the same coordinate plane. How are these two points related?

  1. They are in the same quadrant.
  2. They are reflections across the yy-axis. (correct answer)
  3. They are not related by a reflection because both coordinates changed.
  4. They are reflections across the xx-axis.
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location, with Quadrant I for (+,+), II for (-,+), III for (-,-), and IV for (+,-), and points differing only by signs are reflections across axes. Quadrants are defined as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate for left/right of y-axis (positive right, negative left) and y-coordinate for above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs, like (3,5) and (-3,5) across y-axis (x-sign flip), (3,5) and (3,-5) across x-axis (y-sign flip), or (3,5) and (-3,-5) across origin (both flips). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) to (-3,5) across y-axis, (3,-5) across x-axis, (-3,-5) across origin. Points A(3,5) and E(-3,5) differ only in x-sign, so they are reflections across the y-axis. A common error is claiming they are not related because coordinates changed, or confusing with x-axis reflection. Reflections: identify which sign(s) differ (only x→y-axis reflection, only y→x-axis reflection, both→origin reflection), understand symmetry (reflection creates mirror image across axis). Avoid mistakes like claiming no relationship when signs differ, or reflection changes wrong coordinate.

Question 14

Which sign pattern matches points in Quadrant IV?

  1. x<0, y>0x<0,\ y>0
  2. x>0, y<0x>0,\ y<0 (correct answer)
  3. x>0, y>0x>0,\ y>0
  4. x<0, y<0x<0,\ y<0
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). The sign pattern for Quadrant IV is x>0, y<0, which is choice C. A common error is matching x>0, y<0 to Quadrant II instead of IV, or confusing it with III. To determine the quadrant: (1) check x-sign (positive means right side, quadrants I or IV), (2) check y-sign (negative means lower, quadrants III or IV), (3) combine for IV. Remember quadrant order counterclockwise from upper right, and avoid mistaking sign patterns for wrong quadrants.

Question 15

Based on the coordinate plane, if point TT is reflected to create a point in Quadrant I, which type of reflection was used?

  1. Reflection across the xx-axis only, because the yy-coordinate needed to change sign
  2. Reflection across the yy-axis only, because the xx-coordinate needed to change sign
  3. Reflection across both axes, because both coordinates needed to change signs completely (correct answer)
  4. No reflection is possible, because point TT cannot reach Quadrant I through reflections
Explanation: Point TT is located at (−3,−4)(-3, -4) in Quadrant III, where both coordinates are negative. To reach Quadrant I where both coordinates are positive, both the xx and yy coordinates must change signs. This requires reflection across both axes. Choice A would only change the yy-coordinate sign, resulting in Quadrant II. Choice B would only change the xx-coordinate sign, resulting in Quadrant IV. Choice D is incorrect because reflection across both axes can move any point to any quadrant.

Question 16

A student plots C(−3,−5)C(-3,-5). In which quadrant is point CC located?

  1. Quadrant I
  2. Quadrant II
  3. Quadrant III (correct answer)
  4. Quadrant IV
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location, with Quadrant I for (+,+), II for (-,+), III for (-,-), and IV for (+,-), and points differing only by signs are reflections across axes. Quadrants are defined as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate for left/right of y-axis (positive right, negative left) and y-coordinate for above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs, like (3,5) and (-3,5) across y-axis (x-sign flip), (3,5) and (3,-5) across x-axis (y-sign flip), or (3,5) and (-3,-5) across origin (both flips). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) to (-3,5) across y-axis, (3,-5) across x-axis, (-3,-5) across origin. For point C(-3,-5), both coordinates are negative, placing it in Quadrant III. A common error is confusing quadrants, like thinking (-,-) is Quadrant IV instead of III, or mixing up numbering where II is mistaken for lower left. To determine the quadrant: (1) check x-sign (negative means left side, II or III), (2) check y-sign (negative means lower, III or IV), (3) combine for both negative as III. Remember quadrant order is counterclockwise from upper right: I to II to III to IV, and avoid mistakes like quadrant identification wrong, especially confusing III and IV.

Question 17

A student plots point WW in Quadrant I and then creates three additional points by reflecting WW across the xx-axis (point XX), across the yy-axis (point YY), and across both axes (point ZZ). In which quadrants are points XX, YY, and ZZ located, respectively?

  1. XX in Quadrant II, YY in Quadrant III, ZZ in Quadrant IV
  2. XX in Quadrant IV, YY in Quadrant II, ZZ in Quadrant III (correct answer)
  3. XX in Quadrant III, YY in Quadrant IV, ZZ in Quadrant II
  4. XX in Quadrant II, YY in Quadrant IV, ZZ in Quadrant I
Explanation: Point WW in Quadrant I has positive xx and positive yy coordinates. Reflecting across the xx-axis changes the yy-coordinate sign, so XX has positive xx and negative yy (Quadrant IV). Reflecting across the yy-axis changes the xx-coordinate sign, so YY has negative xx and positive yy (Quadrant II). Reflecting across both axes changes both coordinate signs, so ZZ has negative xx and negative yy (Quadrant III). Choice A incorrectly places XX and YY. Choice C incorrectly places all three points. Choice D incorrectly places YY and ZZ.

Question 18

Two points have coordinates (m,n)(m, n) and (m,−n)(m, -n) where m<0m < 0 and n>0n > 0. After plotting both points, what is true about their positions and quadrant locations?

  1. The first point is in Quadrant IV and the second is in Quadrant I; they are reflections across both axes and have opposite coordinate signs
  2. The first point is in Quadrant III and the second is in Quadrant II; they share the same yy-coordinate and are equidistant from the yy-axis
  3. The first point is in Quadrant I and the second is in Quadrant IV; they are reflections across the origin and share no coordinate values
  4. The first point is in Quadrant II and the second is in Quadrant III; they share the same xx-coordinate and are equidistant from the xx-axis (correct answer)
Explanation: When working with coordinate points and quadrants, you need to remember the sign patterns: Quadrant I (+,+), Quadrant II (-,+), Quadrant III (-,-), and Quadrant IV (+,-). Given the conditions m<0m < 0 and n>0n > 0, let's analyze each point. The first point (m,n)(m, n) has a negative x-coordinate and positive y-coordinate, placing it in Quadrant II. The second point (m,−n)(m, -n) has a negative x-coordinate and negative y-coordinate (since −n<0-n < 0 when n>0n > 0), placing it in Quadrant III. Both points share the same x-coordinate mm, so they lie on the same vertical line. Since one has y-coordinate nn and the other has y-coordinate −n-n, they are equidistant from the x-axis (the same distance above and below it). Choice A incorrectly places the points in Quadrants IV and I, which would require different sign combinations. Choice B correctly identifies the quadrants but wrongly claims they share the same y-coordinate and are equidistant from the y-axis. Choice C places the first point in Quadrant I, which is impossible since m<0m < 0, and incorrectly describes their relationship. Choice D correctly identifies that the first point is in Quadrant II and the second is in Quadrant III, they share the same x-coordinate, and are equidistant from the x-axis. Study tip: Always check the signs of coordinates against the given conditions first, then identify quadrants using the sign patterns. Points with the same x-coordinate form vertical lines, while points with opposite y-coordinates are reflections across the x-axis.

Question 19

A student plots the point A(3,5)A(3,5) on a coordinate plane. Based on the signs of the coordinates, in which quadrant is A(3,5)A(3,5) located?

  1. Quadrant III
  2. Quadrant II
  3. Quadrant I (correct answer)
  4. Quadrant IV
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are defined as I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate x-coordinate shows left/right of y-axis (positive right, negative left), y-coordinate shows above/below x-axis (positive above, negative below); reflections occur when pairs differ only in signs—(3,5) and (-3,5) differ in x-sign (across y-axis), (3,5) and (3,-5) in y-sign (across x-axis), (3,5) and (-3,-5) in both (across origin). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive so Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above) so Quadrant II; reflections include (3,5) across y-axis to (-3,5), across x-axis to (3,-5), across origin to (-3,-5). For point A(3,5), both coordinates are positive, placing it in Quadrant I, which is choice C. A common error is confusing quadrants, like thinking (+,+) is Quadrant II instead of I, or misreading signs and placing it in Quadrant IV. To determine the quadrant: (1) check x-sign (positive means right side, quadrants I or IV), (2) check y-sign (positive means upper, quadrants I or II), (3) combine to both positive for I. Remember quadrant order is counterclockwise from upper right: I to II to III to IV, and avoid mistaking axis points for quadrants.

Question 20

Which sign pattern matches all points in Quadrant IV?​

  1. (−,−)(-, -)
  2. (+,+)(+, +)
  3. (−,+)(-, +)
  4. (+,−)(+, -) (correct answer)
Explanation: This question tests understanding that the signs in ordered pairs indicate quadrant location (I: +,+; II: -,+; III: -,-; IV: +,-), and points differing only by signs are reflections across axes. Quadrants are divided as follows: I (x>0, y>0 upper right both positive), II (x<0, y>0 upper left), III (x<0, y<0 lower left both negative), IV (x>0, y<0 lower right); signs indicate that the x-coordinate sign shows left/right of y-axis (x positive→right, x negative→left), y-coordinate sign shows above/below x-axis (y positive→above, y negative→below); reflections occur when ordered pairs differ only in signs—(3,5) and (-3,5) differ in x-sign only (reflected across y-axis), (3,5) and (3,-5) differ in y-sign (reflected across x-axis), (3,5) and (-3,-5) differ in both (reflected across origin through both axes). For example, (3,5) has x=3>0 (right of y-axis), y=5>0 (above x-axis), both positive→Quadrant I; (-4,2) has x=-4<0 (left), y=2>0 (above)→Quadrant II; reflections: (3,5) across y-axis flips x-sign: (-3,5), across x-axis flips y-sign: (3,-5), across origin flips both: (-3,-5). The sign pattern (+,-) matches all points in Quadrant IV. A common error is selecting (-,+) for Quadrant IV, or confusing patterns like thinking Quadrant IV is both negative. To determine the quadrant: (1) check x-coordinate sign (positive→right side quadrants I or IV, negative→left side II or III), (2) check y-coordinate sign (positive→upper quadrants I or II, negative→lower III or IV), (3) combine (both positive→I, x neg y pos→II, both neg→III, x pos y neg→IV). Quadrant order is counterclockwise from upper right (I→II→III→IV), and mistakes often include quadrant identification wrong, especially confusing II and IV.