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.

Question

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)

Answer 1

Part A: Creating a Number Line

To create a number line for these points, I would draw a horizontal line and mark the center point as zero, which represents the level of the boat. Since we have points above and below this level, I'll label the negative side (to the left of zero) for the depths below the boat and the positive side (to the right of zero) for heights above the boat.

1. Draw a horizontal line and mark a point in the center as "0" to represent the boat.
2. To represent the dolphin, I would move downwards to mark the point at -3.6 yards (3.6 yards below the boat).
3. To represent the fish, I would again move downwards and mark the point at -2.3 yards (2.3 yards below the boat).
4. For the bird, I would move upwards and mark the point at +2.3 yards (2.3 yards above the boat).
5. I would also include evenly spaced ticks on the number line to help visualize distances.

Number Line Representation:

        2.3                0              -2.3              -3.6
         ↑                 |               |                 |
       Bird             Boat             Fish             Dolphin

Part B: What Does Zero Represent?

On my number line, zero represents the level of the boat. It is the reference point from which we measure all other heights and depths. Values above zero indicate distances above the boat (like the bird), while values below zero indicate distances below the boat (like the dolphin and the fish).

Part C: Determining Opposite Points Using Absolute Value

To find which two points are opposites, I can look at their absolute values:

• The dolphin is at -3.6 yards, and its absolute value is |−3.6| = 3.6.
• The fish is at -2.3 yards, and its absolute value is |−2.3| = 2.3.
• The bird is at +2.3 yards, and its absolute value is |2.3| = 2.3.

Now, let's pair the points based on their absolute values:

• The absolute value of the bird (+2.3) is equal to the absolute value of the fish (−2.3). Thus, these two points are opposites because they are equidistant from zero on the number line.

Therefore, the two points that are opposites are the fish (−2.3 yards) and the bird (+2.3 yards).