A leatherback sea turtle was swimming at 850 meters below sea level. He went up 165 meters and then descended 165 meters.

Question

a. Draw a number line to show the change in position of the sea turtle from the depth it was swimming.
b. What integer represents the sea​ turtle's change in​ position?

a. Choose the number line that shows the change in position of the sea turtle.

Answer 1

To represent the movement of the leatherback sea turtle on a number line, we can use the following format, where the negative numbers represent depths below sea level:

1. Start at -850 meters (the initial position of the turtle).
2. The turtle ascends 165 meters, moving to: \(-850 + 165 = -685\) meters.
3. The turtle then descends 165 meters, moving back down to: \(-685 - 165 = -850\) meters.

a. Number Line Representation:

You can visualize the number line as follows:

-900     -800      -700      -600
 |---------|---------|---------|
                ↑
              -850 (Initial position)

After moving up:

-900     -800      -700      -600
 |---------|---------|---------|
                 ↑
              -685 (After moving up 165 m)

After moving down:

-900     -800      -700      -600
 |---------|---------|---------|
                ↑
              -850 (Back to initial position)

b. Integer Representing the Turtle's Change in Position:

To find the integer that represents the sea turtle's change in position:

1. Initial position: -850 meters.
2. After going up 165 meters: -685 meters.
3. After going down 165 meters: -850 meters.

The change in position can be calculated as follows:

• From -850 to -685 (up): change = \(165\)
• From -685 to -850 (down): change = \(-165\)

The overall change in position from its original depth is back to \(0\), as it returned to the same depth of -850 meters, thus the total change can be calculated as: \[ \text{Change in position} = Final Position - Initial Position = -850 - (-850) = 0 \]

So the integer representing the turtle's overall change in position is 0.