6th Grade Math Quiz: Understand Signs In Coordinate Plane
20 questions · exam conditions
0:00
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
← Back to quizzes

6th Grade Math Quiz

6th Grade Math Quiz: Understand Signs In Coordinate Plane

Practice Understand Signs In Coordinate Plane in 6th Grade 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 6th Grade Math.

How to use this quiz

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.

All questions

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

A student plots the point (−4,2)(-4,2) for a science lab setup. In which quadrant is (−4,2)(-4,2) located?​

  1. Quadrant II (correct answer)
  2. Quadrant I
  3. Quadrant III
  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 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 (-4,2) is in Quadrant II because x is negative and y is positive. A common error is identifying (-,+) as Quadrant III instead of II, or confusing quadrant numbering like thinking II is lower 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 II and IV.

Question 3

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 III
  3. Quadrant I (correct answer)
  4. Quadrant II
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 4

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 5

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.

Question 6

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

  1. (3,−5)(3,-5)
  2. (−3,−5)(-3,-5)
  3. (5,3)(5,3)
  4. (−3,5)(-3,5) (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 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 y-axis flips the x-sign to (-3,5), which is choice A. A common error is flipping the y-sign instead for y-axis reflection, or confusing it with origin reflection. Reflections: identify which sign differs (only x for y-axis), understand symmetry as mirror image across axis. Mistakes include changing the wrong coordinate for the reflection or claiming no relationship when signs differ.

Question 7

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 8

A point has coordinates with x<0x<0 and y>0y>0. Which quadrant must the point be in?​

  1. Quadrant III
  2. Quadrant IV
  3. Quadrant I
  4. Quadrant II (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). A point with x<0 and y>0 must be in Quadrant II. A common error is claiming such a point is in Quadrant III, or confusing signs like thinking negative x means below x-axis. 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.

Question 9

A point has coordinates with x<0x<0 and y>0y>0. Which quadrant must the point be in?

  1. Quadrant II (correct answer)
  2. Quadrant III
  3. Quadrant I
  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 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). A point with x<0 and y>0 must be in Quadrant II. A common error is claiming such a point is in Quadrant III, or confusing signs like thinking negative x means below x-axis. 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.

Question 10

A student plots the point (−4,2)(-4,2) for a science lab setup. In which quadrant is (−4,2)(-4,2) located?

  1. Quadrant IV
  2. Quadrant I
  3. Quadrant II (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 (-4,2) is in Quadrant II because x is negative and y is positive. A common error is identifying (-,+) as Quadrant III instead of II, or confusing quadrant numbering like thinking II is lower 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 II and IV.

Question 11

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

  1. Quadrant I
  2. Quadrant III (correct answer)
  3. Quadrant II
  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 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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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.