**Correct Option: A. 5 meters** ### Step-by-Step Explanation 1. **Understanding Displacement**: Displacement is defined as the shortest distance from the initial position to the final position, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. 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 increases the x-coordinate, and moving north increases the y-coordinate. 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) 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: \[ d = \sqrt{(3 \, \text{m})^2 + (4 \, \text{m})^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{meters} \] 5. **Conclusion**: The displacement from the starting point to the final position is **5 meters** in a direction that can be described as northeast. ### Why Other Options Are Incorrect - **Option B (7 meters)**: This option does not represent the shortest distance between the starting and ending points. It may confuse the total distance traveled (3 m + 4 m = 7 m) with displacement, which is not the same. - **Option C (1 meter)**: This option is incorrect as it does not reflect any calculation related to the actual movement. The displacement cannot be less than either of the legs of the triangle formed by the movements. - **Option D (12 meters)**: This option also misrepresents the situation. It could be a misunderstanding of total distance traveled (3 m + 4 m + 5 m = 12 m), but again, this is not the displacement. ### Common Pitfalls - Confusing total distance traveled with displacement. Remember, displacement is the straight-line distance from the start to the end point. - Forgetting to apply the Pythagorean theorem correctly. Ensure you are using the correct sides of the triangle formed by the movements. ### Revision Summary - Displacement is the shortest distance from the starting point to the final position. - Use the Pythagorean theorem to calculate displacement when movements are at right angles. - The correct displacement in this scenario is 5 meters. - Always differentiate between total distance traveled and displacement.