**Correct Option: A. 5 meters** ### Step-by-Step Explanation 1. **Understanding Displacement**: Displacement is a vector quantity that refers to the shortest distance from the initial position to the final position, along with the direction. It is different from distance, which is a scalar quantity that only considers the total path traveled. 2. **Visualizing the Movement**: - The person first walks **3 meters east**. - Then, they walk **4 meters north**. - To visualize this, imagine a coordinate system where the starting point is at the origin (0,0). Moving east means moving along the x-axis, and moving north means moving along the y-axis. 3. **Calculating the Final Position**: - After walking 3 meters east, the new position is (3, 0). - After walking 4 meters north from (3, 0), the final position is (3, 4). 4. **Using the Pythagorean Theorem**: - To find the displacement, we can treat the movement as a right triangle where: - One leg (eastward movement) is 3 meters. - The other leg (northward movement) is 4 meters. - The displacement (hypotenuse of the triangle) can be calculated using the Pythagorean theorem: \[ d = \sqrt{x^2 + y^2} \] where \(x\) is the eastward distance and \(y\) is the northward distance. - Plugging in the values: \[ d = \sqrt{(3 \, \text{m})^2 + (4 \, \text{m})^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{m} \] 5. **Conclusion**: The total displacement from the starting point to the final position is **5 meters**. ### Explanation of Other Options - **Option B (7 meters)**: This option might confuse distance traveled with displacement. The total distance walked is 3 meters + 4 meters = 7 meters, but this is not the displacement, which is the straight-line distance from start to finish. - **Option C (12 meters)**: This option likely results from misunderstanding the path taken. It could be mistakenly calculated by adding the two distances walked (3 + 4 + 5), but this does not apply to displacement. - **Option D (1 meter)**: This option is incorrect as it does not reflect any logical calculation based on the movements described. It may arise from a misunderstanding of how to calculate displacement. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path length, while displacement is the straight-line distance from start to finish. - Forgetting to use the Pythagorean theorem for right triangles: Always check if the movements form a right triangle when calculating displacement. ### Revision Summary - Displacement is the shortest distance from the starting point to the final position, considering direction. - Use the Pythagorean theorem to calculate displacement when movements form a right triangle. - The correct displacement for the given movements (3 meters east and 4 meters north) is 5 meters. - Always differentiate between total distance traveled and displacement in physics problems.