Use the image to answer the question.

Question

A vertical number line starting at negative 10 on the bottom of the line with tick marks every one unit up to positive 10 at the top. The point negative 1.2 is labeled.

What does the absolute value of the point labeled in the image mean if the number line represents temperature change?

The temperature decreased 1.2 degrees.
 The temperature increased 1.2 degrees.
 There was no change in temperature.
 The temperature equals 1.2 degrees.
Question 4(Multiple Choice Worth 2 points)
(Opposites and Absolute Value LC)

Seven rational numbers are plotted on a number line.

A number line starting at negative 2.5 with tick marks every 0.25 up to positive 2.5. Point A is located at negative 2. Point B is located at negative 1.5. Point C is located at negative 0.5. Point D is located at 0. Point E is located at 0.5. Point F is located at 1.5. Point G is located at 2.

Which point represents the opposite of Point C?

B
 E
 F
 G
Question 5(Multiple Choice Worth 2 points)
(Opposites and Absolute Value MC)

Eight rational numbers are plotted on a number line.

A number line with Point A labeled at negative three halves. Point B is labeled at negative four thirds. Point C is labeled at negative three fourths. Point D is labeled at negative two thirds. Point E is labeled at two thirds. Point F is labeled at three fourths. Point G is labeled at four thirds. Point H is labeled at three halves.

Which of the following is true about opposite numbers?

Point D and Point A are opposite rational numbers because they are the reciprocal of each other.
 Point D and Point E are opposite rational numbers because they are the same distance away from zero.
 Point D and Point H are opposite rational numbers because they are the opposite reciprocals of each other.
 Point D and Point F are opposite rational numbers because Point F is farther away from zero than Point D.
Question 6 (Essay Worth 4 points)
(Opposites and Absolute Value HC)

A passenger on a boat notices that there is a dolphin 3.6 yards below the boat. There is also a fish 2.3 yards below the boat. They also see a bird that is 2.3 yards above the boat.

Part A: Explain how you would create a number line for these points. (1 point)

Part B: What does zero represent on your number line? (1 point)

Part C: Determine which two points are opposites, using absolute value. Be sure to show your work. (2 points)

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FDK191.12

GPT-4o mini · Answer

To address your questions: **Question 1:** The absolute value of the point labeled, in this case -1.2, represents the distance of that point from zero on the number line, regardless of direction. Since the number line represents temperature change, the absolute value signifies how much the temperature has changed without considering the direction (increase or decrease). **Answer:** The temperature decreased 1.2 degrees. --- **Question 4:** To find the opposite of Point C, which is at -0.5, we look for the point that is at the same distance from zero but in the opposite direction. Therefore, the opposite of -0.5 is 0.5, which corresponds to Point E. **Answer:** E --- **Question 5:** To identify which pairs are opposite numbers, we look for points that have the same distance from zero but are on opposite sides of the number line. - Point D (-2/3) and Point E (2/3) are equal distances from zero (2/3), therefore they are opposites. So we can conclude that **Point D and Point E are opposite rational numbers.** **Answer:** Point D and Point E are opposite rational numbers because they are the same distance away from zero. --- **Question 6:** **Part A:** To create a number line for these points, start by marking zero, which represents the surface of the water. Then, mark points for -3.6 (for the dolphin) and -2.3 (for the fish) below zero. For the bird, mark +2.3 above zero on the number line. You could label each tick mark to indicate the distance from zero. **Part B:** Zero on the number line represents the surface of the water. It is the point where everything below it is underwater (negative values) and everything above it is above the water's surface (positive values). **Part C:** The two points that are opposites are the fish and the bird. The fish is at -2.3 yards and the bird is at +2.3 yards. Their absolute values are both 2.3, which means they are the same distance from zero but in opposite directions. - Work shown: Absolute value of the fish: | -2.3 | = 2.3 Absolute value of the bird: | 2.3 | = 2.3 Thus, the points -2.3 and +2.3 are opposites. --- If you have further questions or need additional clarification, feel free to ask!