Middle School Math Quiz: Understand Opposites On Number Line
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Understand Opposites On Number LineQuestion 1 of 20

A pattern on a number line shows: 5→−5→5→−5→?5 \to -5 \to 5 \to -5 \to ? If this pattern continues by repeatedly applying the opposite operation, what number will appear in the 10th position of this sequence?

5050, because you multiply the original number by the position number
55, because the sequence returns to the starting value every two steps
−5-5, because the 10th position corresponds to an even-numbered step
00, because after many opposite operations the result approaches zero
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Middle School Math Quiz

Middle School Math Quiz: Understand Opposites On Number Line

Practice Understand Opposites On Number Line 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 Opposites On Number Line, 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

A pattern on a number line shows: 5→−5→5→−5→?5 \to -5 \to 5 \to -5 \to ? If this pattern continues by repeatedly applying the opposite operation, what number will appear in the 10th position of this sequence?

  1. 5050, because you multiply the original number by the position number
  2. 55, because the sequence returns to the starting value every two steps
  3. −5-5, because the 10th position corresponds to an even-numbered step (correct answer)
  4. 00, because after many opposite operations the result approaches zero
Explanation: When you encounter a repeating pattern question, you need to identify the rule and determine where in the cycle a specific position falls. This sequence shows numbers alternating between positive and negative by applying the "opposite" operation (multiplying by -1). Let's trace the pattern: Position 1 is 55, position 2 is −5-5, position 3 is 55, position 4 is −5-5, and so on. The pattern repeats every 2 positions. To find the 10th position, you need to determine whether 10 corresponds to an odd position (which gives 55) or an even position (which gives −5-5). Since 10 is even, the 10th position will be −5-5. Answer A is wrong because you don't multiply by position numbers—you're applying the opposite operation repeatedly. The sequence doesn't grow larger; it just alternates. Answer B incorrectly identifies what happens at even positions. While it's true the pattern repeats every two steps, position 10 doesn't return to the starting value of 55—it lands on −5-5. Answer D misunderstands what "opposite operation" means. Taking the opposite of a number (multiplying by -1) doesn't make values approach zero; it just flips the sign. For repeating pattern problems, always identify the cycle length first, then use division to find where your target position falls within that cycle. Here, odd positions give the original number, even positions give its opposite.

Question 2

Which statement is always true for any integer aa (from −20-20 to 2020) on a number line?

  1. If aa is negative, then its opposite is also negative.
  2. The opposite of 0 does not exist.
  3. The opposite of aa is always aa.
  4. −(−a)=a-(-a)=a. (correct answer)
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3) flips -3 to 3, and −(−10)=10, always following -(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like |5|=5 and |-5|=5, both 5 units from 0. The statement -(-a)=a is always true for any integer a, as in choice B, because double opposites return to the original. A common error is thinking opposites of negatives stay negative or that 0 has no opposite, but these violate the properties of opposites.

Question 3

A diver's position is measured relative to sea level (00). If the diver is at −9-9 meters, which number represents the diver's opposite position (same distance from sea level, but above it)?

  1. −9-9
  2. 00
  3. 99 (correct answer)
  4. −18-18
Explanation: This question tests applying the concept of opposites to a real-world context where positions are measured relative to a reference point (sea level = 0). If the diver is at -9 meters (9 meters below sea level), the opposite position is 9 meters above sea level, which is represented by the positive number 9. For example, -5 meters below sea level has opposite position 5 meters above sea level; -12 feet below ground has opposite 12 feet above ground; the pattern is that negative depths have positive height opposites. The diver at -9 meters is 9 units below 0 (sea level), so the opposite position is 9 units above 0, which is 9 meters. Common mistakes include keeping the negative sign (-9), doubling the distance (-18), or thinking 0 is involved when it represents sea level, not the answer. To solve: (1) identify current position (-9, below sea level), (2) find opposite by changing sign (positive 9), (3) interpret as 9 meters above sea level. This demonstrates how opposites represent symmetric positions around a reference point in real-world measurements.

Question 4

A student says, "−(−7)=−7-(-7) = -7." Which value correctly evaluates −(−7)-(-7)?

  1. 00
  2. −7-7
  3. 1414
  4. 77 (correct answer)
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and equidistant positions, understanding that the opposite of the opposite returns to the original like −(−3)=3, and zero as its own opposite. Opposites are numbers with opposite signs equidistant from 0 on the number line, such as 5 being 5 units right of 0 and -5 being 5 units left, making them opposites on opposite sides; the opposite of the opposite involves flipping the sign twice to return to the original, so −(−3) flips -3 to 3 and always -(-a)=a; zero is special as the opposite of 0 is 0, the only number equal to its own opposite since 0 is neither positive nor negative; opposites have equal distance from zero, with |5|=5 and |-5|=5, both 5 units from 0. For example, 7 and -7 are opposites with 7 to the right of 0 and -7 to the left, each at an equal distance of 7 from zero; the opposite of -3 is -(-3)=3, flipping to positive; the opposite of 0 is 0, the only number unchanged by flipping sign; imagine a number line showing -5, 0, +5 with -5 and +5 equidistant from center 0. The correct evaluation of -(-7) is 7, as it flips the sign twice back to positive, making choice C right and correcting the student's error. A common error is not flipping back, like -(-3)=-3, or confusing with zero or doubling to 14. To recognize opposites: the opposite of a positive is negative, so opposite of 5 is -5 by flipping the sign; the opposite of a negative is positive, so opposite of -3 is 3; the opposite of 0 is 0, a unique property; and on the number line, opposites are on opposite sides of 0 at equal distances. The property -(-a)=a always holds as a double negative returns to the original, like -(-7)=7, true for any number; opposites have the same absolute value for distance from 0, |a|=|-a| such as |8|=|-8|=8, making them equidistant; this helps understand number line symmetry and operations like adding an opposite to get zero, a+(-a)=0; avoid mistakes like -(-a)=-a error or thinking 0 has a different opposite.

Question 5

On a number line, a value of +6+6 is 6 units to the right of 0. Which number is the opposite of +6+6?

  1. 00
  2. −12-12
  3. −6-6 (correct answer)
  4. 66
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3) flips -3 to 3, and −(−10)=10, always following -(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like |5|=5 and |-5|=5, both 5 units from 0. For +6, which is 6 units to the right of 0, its opposite is -6, 6 units to the left of 0, so choice B is correct. A common mistake is thinking the opposite is twice the distance, like -12, but opposites are always the same distance on the opposite side.

Question 6

Compare the distances from 00: ∣5∣|5| and ∣−5∣|-5|. Which statement is true?

  1. ∣−5∣=−5|-5| = -5
  2. ∣5∣<∣−5∣|5| < |-5|
  3. ∣5∣>∣−5∣|5| > |-5|
  4. ∣5∣=∣−5∣|5| = |-5| (correct answer)
Explanation: This question tests understanding that opposites have equal absolute values, meaning they're the same distance from 0 on the number line. The absolute value |a| represents the distance from 0, regardless of direction: |5| = 5 (distance of 5 from 0) and |-5| = 5 (also distance of 5 from 0), so opposites always have equal absolute values. For example, |7| = |-7| = 7 (both are 7 units from 0), |−3| = |3| = 3 (both are 3 units from 0), demonstrating that opposite numbers have the same distance from 0. The correct answer is |5| = |-5| because both equal 5, representing the same distance from 0 on the number line. Common errors include thinking negative numbers have greater distance (|5| < |-5|), positive numbers have greater distance (|5| > |-5|), or that |-5| equals -5 (confusing absolute value with the number itself). Key concept: absolute value removes the sign and gives distance, so |a| = |-a| for any number a. This property confirms that opposites are equidistant from 0, just on different sides of the number line.

Question 7

Use the number line shown. Points MM, NN, and PP represent three consecutive applications of the opposite operation, starting with MM at 22. Which statement correctly describes the relationship between these points?

  1. Points MM and PP are at the same location, while NN is equidistant from both (correct answer)
  2. Point PP is twice as far from zero as point MM, but on the same side
  3. Points MM, NN, and PP are evenly spaced along the number line
  4. Point NN is at the opposite of MM, and PP is at the opposite of zero
Explanation: Starting at M=2M = 2: First opposite gives N=−2N = -2. Second opposite gives P=2P = 2. So MM and PP are both at position 22, while NN is at −2-2, equidistant from both MM and PP. Choice B incorrectly calculates PP's position. Choice C incorrectly assumes equal spacing. Choice D incorrectly places PP at 00.

Question 8

Refer to the number line. If point AA represents −3-3 and point BB represents the opposite of point AA, which statement about the opposite of point BB is correct?

  1. The opposite of point BB is located 66 units to the left of point BB
  2. The opposite of point BB is located at the same position as point AA (correct answer)
  3. The opposite of point BB is located at position 66 on the number line
  4. The opposite of point BB is located exactly halfway between points AA and BB
Explanation: Point AA is at −3-3. Point BB (opposite of AA) is at 33. The opposite of point BB is the opposite of 33, which is −3-3, the same as point AA. This demonstrates that the opposite of the opposite returns to the original number. Choice A gives the correct distance but wrong direction. Choice C incorrectly doubles the position. Choice D incorrectly places it at 00.

Question 9

Marcus is playing a number game where he starts at −5-5 on a number line. He moves to the opposite of his current position, then moves to the opposite of that new position. If he repeats this process one more time (moving to the opposite twice more), what is his final position?

  1. −5-5 (correct answer)
  2. 55
  3. 00
  4. 1010
Explanation: Starting at −5-5: First move to opposite: 55. Second move to opposite: −5-5. Third move to opposite: 55. Fourth move to opposite: −5-5. Since the opposite of the opposite returns to the original number, moving to the opposite an even number of times returns to the starting position. Choice B would be correct after an odd number of moves. Choice C incorrectly assumes all moves lead to zero. Choice D incorrectly doubles the starting position.

Question 10

A classroom number line shows integers from −10-10 to 1010 with 00 in the center. Which pair of numbers are opposites (on opposite sides of 00 and the same distance from 00)?

  1. 55 and 66
  2. 33 and −2-2
  3. 44 and −4-4 (correct answer)
  4. −6-6 and −6-6
Explanation: This question tests recognizing opposites on a number line, where opposites have opposite signs and are equidistant from 0. Opposites are numbers with opposite signs that are the same distance from 0 on the number line (like 4 and -4, where 4 is 4 units right of 0 and -4 is 4 units left). For example, 7 and -7 are opposites because they're both 7 units from 0 but on opposite sides; 3 and -2 are not opposites because they have different distances from 0 (3 units vs 2 units). Option B shows 4 and -4, which are opposites: 4 is positive (right of 0) and -4 is negative (left of 0), both exactly 4 units from 0. Common errors include choosing pairs with the same sign like -6 and -6 (both negative, on same side of 0), pairs with different distances like 3 and -2, or positive pairs like 5 and 6. To identify opposites: (1) check opposite signs (one positive, one negative), (2) verify equal distance from 0 (|4| = |-4| = 4), (3) confirm they're on opposite sides of 0. The key property is that opposites always sum to 0 (4 + (-4) = 0), which helps verify the correct answer.

Question 11

On a number line, three points are marked: XX at −4-4, YY at the opposite of XX, and ZZ at the opposite of the opposite of XX. If you walk from point YY to point ZZ, in which direction do you move and how far?

  1. 00 units, because points YY and ZZ are at the same location
  2. 44 units to the right, because you move from 00 to 44
  3. 88 units to the right, because you move from −4-4 to 44
  4. 88 units to the left, because you move from 44 to −4-4 (correct answer)
Explanation: When you see a question about "opposites" on a number line, you're working with the concept that opposite numbers are the same distance from zero but on different sides. The opposite of any number aa is −a-a. Let's find each point's location step by step. Point XX is at −4-4. The opposite of XX means the opposite of −4-4, which is 44. So point YY is at 44. Now for point ZZ: it's at the opposite of the opposite of XX. The opposite of XX is 44, so the opposite of that is −4-4. Therefore, point ZZ is at −4-4. Walking from point YY at 44 to point ZZ at −4-4 means moving from 44 to −4-4. This is 88 units to the left, confirming answer D. Let's examine why the other answers miss the mark. Choice A incorrectly assumes YY and ZZ are at the same location, but YY is at 44 while ZZ is at −4-4. Choice B places point YY at 00 instead of 44, misunderstanding what "opposite of −4-4" means. Choice C has the right distance of 88 units but gets the direction backwards—it describes moving from −4-4 to 44 instead of from 44 to −4-4. Remember: when finding the opposite of a negative number, you get a positive number, and vice versa. Also, "opposite of the opposite" brings you back to where you started—so XX and ZZ end up at the same location.

Question 12

Sarah claims that 00 is the opposite of itself because it's the only number that equals its own opposite. To verify this, she checks whether −(0)=0-(0) = 0. Which reasoning best explains why Sarah's claim is correct?

  1. Zero is equidistant from all positive and negative numbers on the number line
  2. Zero has no sign, so applying the opposite operation leaves it unchanged (correct answer)
  3. Zero is located at the center point that separates opposites on the number line
  4. Zero is the only number that is the same distance from itself as from its opposite
Explanation: The opposite of 00 is −0-0, which equals 00 because zero has no sign to change. This makes 00 unique among all numbers as being its own opposite. Choice A incorrectly describes distance relationships. Choice C describes zero's location but not why it's its own opposite. Choice D creates a circular definition that doesn't explain the concept.

Question 13

A student writes the expression −(−(−(−6)))-(-(-(-6))) and claims it equals 66 because 'four negatives make a positive.' Which error in reasoning should be corrected?

  1. The student should work from outside in: the first negative makes everything negative
  2. The student should count that there are actually only three negative signs, making the result −6-6
  3. The student should work from inside out: −6→6→−6→6-6 \to 6 \to -6 \to 6, confirming the result is 66 (correct answer)
  4. The student should recognize that nested negatives don't follow the same rules as multiplication
Explanation: When you encounter nested negative signs like −(−(−(−6)))-(-(-(-6))), you need to evaluate them step by step from the inside out, just like with parentheses in order of operations. Let's work through this expression systematically: Start with the innermost value, −6-6. Then apply each negative sign one at a time moving outward. The first negative sign gives us −(−6)=6-(-6) = 6. The next negative sign gives us −(6)=−6-(6) = -6. Finally, the outermost negative sign gives us −(−6)=6-(-6) = 6. So the correct sequence is −6→6→−6→6-6 \to 6 \to -6 \to 6, and the final answer is indeed 66. Choice C correctly describes this inside-out process and confirms the result is 66, making it the right answer. Choice A is wrong because working "outside in" isn't how we evaluate mathematical expressions—we always work from the innermost operations outward. Choice B incorrectly suggests there are only three negative signs when there are actually four, and even if there were three, the student's reasoning about "counting negatives" is flawed. Choice D is incorrect because nested negatives do follow consistent mathematical rules—you just need to apply them systematically rather than trying to count them all at once. The key insight is that while the student got the right answer, their reasoning of "four negatives make a positive" oversimplifies the process. Remember: always evaluate nested operations from the inside out, applying one operation at a time.

Question 14

A student marks 33 on a number line. Where should the student mark −3-3 so that 33 and −3-3 are opposites?

  1. On the same point as 33
  2. Three units to the left of 00 (correct answer)
  3. Three units to the right of 00
  4. At 00, because 00 is the opposite of every number
Explanation: This question tests understanding how to position opposites on a number line: they must be on opposite sides of 0 and equidistant from it. If 3 is marked (3 units right of 0), then -3 must be 3 units left of 0 to be its opposite, creating symmetry around 0. For example, if 5 is marked 5 units right of 0, then -5 goes 5 units left of 0; if -7 is marked 7 units left, then 7 goes 7 units right; opposites mirror each other across 0. To place -3 as the opposite of 3, it must be three units to the left of 0, making them equidistant but on opposite sides. Common mistakes include placing -3 on the same point as 3 (same position, not opposite), three units right of 0 (same side as 3), or at 0 (confusing 0's role as center point with being everyone's opposite). The key visualization: 3 is three steps right from 0, so -3 is three steps left from 0, creating perfect symmetry. This demonstrates that opposites are reflections across 0 on the number line, maintaining equal distance but opposite direction.

Question 15

Evaluate: −(−7)-(-7). (This is the opposite of the opposite of 77.)

  1. 77 (correct answer)
  2. 1414
  3. 00
  4. −7-7
Explanation: This question tests evaluating the opposite of an opposite, which always returns to the original number due to the property -(-a) = a. The expression -(-7) means "the opposite of the opposite of 7": first we find the opposite of 7 (which is -7), then find the opposite of that result (-7), which gives us 7. For example, -(-3) = 3 (opposite of -3 is 3), -(-10) = 10 (opposite of -10 is 10), and this pattern -(-a) = a works for any number. Evaluating -(-7): the inner negative makes 7 become -7, then the outer negative makes -7 become 7, so -(-7) = 7. Common errors include thinking double negatives stay negative (-(-7) = -7), adding the values (-(-7) = -14), or confusing with zero. The key insight is that applying the opposite operation twice returns you to where you started: if you flip a number's sign twice, you get back the original number. This fundamental property helps simplify expressions and understand that negation is its own inverse operation.

Question 16

Which number is the opposite of 0 on a number line?

  1. 00 (correct answer)
  2. There is no opposite of 0.
  3. −0-0 (a different number than 0)
  4. 11
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3) flips -3 to 3, and −(−10)=10, always following -(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like |5|=5 and |-5|=5, both 5 units from 0. The opposite of 0 is 0, as in choice C, because it's at the center and flipping its sign doesn't change it. A common error is thinking the opposite of 0 is undefined or a different number like 1, but zero is uniquely its own opposite.

Question 17

On a number line, which pair of numbers are opposites?

  1. −5-5 and −5-5
  2. −4-4 and 55
  3. −5-5 and 55 (correct answer)
  4. 55 and 00
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3) flips -3 to 3, and −(−10)=10, always following -(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like |5|=5 and |-5|=5, both 5 units from 0. The pair -5 and 5 are opposites because they have opposite signs and the same distance from 0, so choice A is correct. A common mistake is pairing numbers like -4 and 5, which have different distances from 0, or thinking opposites are the same number like -5 and -5.

Question 18

A number line is shown from −10-10 to 1010 with 0 in the center. Point AA is at 55. Where is the opposite of point AA located?

  1. At 55, 5 units to the left of 0
  2. At −5-5, 5 units to the left of 0 (correct answer)
  3. At −5-5, 5 units to the right of 0
  4. At 00, because opposites meet at 0
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3-(-3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3)-(-3) flips -3 to 3, and −(−10)=10-(-10)=10, always following −(−a)=a-(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like ∣5∣=5|5|=5 and ∣−5∣=5|-5|=5, both 5 units from 0. The opposite of 5 is at -5, 5 units to the left of 0, so choice A is correct. A common mistake is confusing directions, like saying -5 is to the right, but negatives are always left of 0 on a standard number line.

Question 19

A student says, "−(−4)=−4-(-4) = -4." Which choice correctly evaluates −(−4)-(-4)?

  1. 00
  2. −8-8
  3. −4-4
  4. 44 (correct answer)
Explanation: This question tests recognizing opposites on a number line, where opposite signs indicate opposite sides of 0 and they are equidistant, understanding that the opposite of the opposite returns to the original like −(−3)=3, and that zero is its own opposite. Opposites are numbers with opposite signs that are equidistant from 0 on the number line; for example, 5 is 5 units to the right of 0, and -5 is 5 units to the left, so they are opposites on opposite sides. The opposite of the opposite involves flipping the sign twice, which returns to the original number, such as −(−3) flips -3 to 3, and −(−10)=10, always following -(-a)=a. Zero is special because the opposite of 0 is 0, as it's the only number equal to its own opposite and is neither positive nor negative. Distance is key, as opposites have equal distance from zero, like |5|=5 and |-5|=5, both 5 units from 0. Evaluating -(-4) correctly gives 4, as in choice B, because two sign flips return to positive. A common mistake is thinking -(-4) = -4, not understanding that double negatives cancel out.

Question 20

On a number line, the opposite of a number is the same distance from 00 but on the other side. What is the opposite of −12-12?

  1. 1212 (correct answer)
  2. −12-12
  3. 00
  4. −11-11
Explanation: This question tests understanding that the opposite of a number is found by changing its sign while maintaining the same distance from 0. Opposites are numbers equidistant from 0 but on opposite sides of the number line: if -12 is 12 units left of 0, its opposite is 12 units right of 0, which is 12. For example, the opposite of -5 is 5 (changes from negative to positive), the opposite of 8 is -8 (changes from positive to negative), and the opposite of 0 is 0 (special case). The opposite of -12 is 12 because we flip the sign from negative to positive while keeping the distance of 12 units from 0. Common mistakes include keeping the same sign (thinking opposite of -12 is -12), changing the magnitude (like -11), or thinking 0 is involved when it's not. To find opposites: (1) identify the sign (negative for -12), (2) flip to opposite sign (positive), (3) keep same distance from 0 (12 units), resulting in 12. This reflects the symmetry of the number line where every negative number has a positive counterpart the same distance from 0.