The correct option is **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 how much ground an object has covered. 2. **Visualizing the Movement**: - The person walks **3 meters east** and then **4 meters north**. - If we visualize this on a coordinate plane, we can represent the starting point as the origin (0, 0). - Moving 3 meters east takes the person to the point (3, 0). - From there, moving 4 meters north takes the person to the point (3, 4). 3. **Calculating Displacement**: - To find the displacement, we need to determine the straight-line distance from the starting point (0, 0) to the final position (3, 4). - We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. - Here, the eastward movement (3 meters) and the northward movement (4 meters) form the two sides of a right triangle. The formula for the hypotenuse \(d\) (displacement) is: \[ d = \sqrt{(x^2 + y^2)} \] where \(x\) is the eastward distance and \(y\) is the northward distance. Plugging in the values: \[ d = \sqrt{(3^2 + 4^2)} = \sqrt{(9 + 16)} = \sqrt{25} = 5 \text{ meters} \] 4. **Conclusion**: The total 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 might confuse distance with displacement. The total distance traveled (3 meters east + 4 meters north = 7 meters) is not the same as displacement, which is the straight-line distance. - **Option C (12 meters)**: This option is incorrect because it does not represent any relevant calculation related to the movements described. It could be a misunderstanding of adding distances or a miscalculation. - **Option D (1 meter)**: This option is incorrect as it significantly underestimates the displacement. It does not take into account the actual distances traveled in both directions. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path length traveled, while displacement is the shortest path between two points. - Misapplying the Pythagorean theorem: Ensure that you are using the correct sides of the triangle formed by the movements. - Forgetting to consider direction: Displacement is a vector, so it has both magnitude and direction. ### Revision Summary - Displacement is the shortest distance from the initial to the final position. - Use the Pythagorean theorem to calculate displacement when movements are perpendicular. - The correct displacement for a 3-meter east and 4-meter north movement is 5 meters. - Always differentiate between distance (scalar) and displacement (vector).