Final answer:
The distance traveled is the sum of the movements north and west, totaling 21 meters, while the displacement is calculated using the Pythagorean theorem to be 15 meters, making option A correct.
Step-by-step explanation:
If you move 9 meters north and then 12 meters west, you cover two segments of a right-angled triangle, where the northward movement represents one leg and the westward movement represents the other leg.
The distance you've covered is simply the sum of these two movements, which is 9 meters + 12 meters = 21 meters.
The displacement, on the other hand, is the straight-line distance from your starting point to your final position. To find the displacement, we use the Pythagorean theorem. This means:
Displacement = √((9 m)^2 + (12 m)^2)
Displacement = √(81 m^2 + 144 m^2)
Displacement = √(225 m^2)
Displacement = 15 meters
Therefore, the correct option is:
A) Distance = 21 meters, Displacement = 15 meters