To determine which situation describes opposite quantities that, when combined, would equal 0, we need to identify the situation where the family returns to their original position by making two equal and opposite movements.
Let's examine each option:
a. A family rides their bikes four miles due north from home, then they ride their bikes four miles due east.
- The family is now 4 miles north and 4 miles east from home. They are not at home.
b. A family rides their bikes four miles due east from home, then they ride their bikes four miles due west.
- The family rides 4 miles east, then rides 4 miles back west, returning to the starting point (home). This situation has opposite movements that result in a net displacement of 0.
c. A family rides their bikes four miles due north from home, then they ride their bikes four miles due west.
- The family is now 4 miles north and 4 miles west from home. They are not at home.
d. A family rides their bikes four miles due east from home, then they ride their bikes four miles due south.
- The family is now 4 miles east and 4 miles south from home. They are not at home.
Conclusion: The correct answer is b, where the family rides 4 miles east and then 4 miles west, resulting in a total displacement of 0.