**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 how much ground an object has covered. 2. **Visualizing the Movement**: - The person first walks **3 meters east**. We can represent this movement on a coordinate system where east is the positive x-direction. - Next, the person walks **4 meters north**. In our coordinate system, north is the positive y-direction. 3. **Setting Up the Coordinates**: - Starting point (initial position) can be considered as the origin (0, 0). - 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. **Calculating Displacement**: - To find the displacement, we need to calculate 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 (displacement in this case) is equal to the sum of the squares of the other two sides. \[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where \((x_1, y_1)\) is the starting point and \((x_2, y_2)\) is the final position. Plugging in the coordinates: \[ \text{Displacement} = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ meters} \] 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 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: 1 meter**: This option is incorrect as it does not represent any calculation related to the movements made. It is far less than the actual displacement calculated. - **Option D: 12 meters**: This option also confuses total distance with displacement. It does not relate to the actual movements made and is not derived from any calculation relevant to the problem. ### 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 coordinates and that you are calculating the hypotenuse correctly. ### Revision Summary - Displacement is the shortest distance from the starting point to the final position, considering direction. - Use the Pythagorean theorem to calculate displacement in two-dimensional movements. - 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.