Question
A leatherback sea turtle was swimming at 850 meters below sea level. He went up 165 meters and then descended 165 meters.
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.
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.
Answers
GPT-4o mini
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**.
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**.