**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 **4 meters east**. We can represent this movement on a coordinate system where east is the positive x-direction. - Next, the person walks **3 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 4 meters east, the new position is (4, 0). - After walking 3 meters north from (4, 0), the final position is (4, 3). 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 (4, 3). - 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 initial position and \((x_2, y_2)\) is the final position. Plugging in the coordinates: \[ \text{Displacement} = \sqrt{(4 - 0)^2 + (3 - 0)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ meters} \] 5. **Conclusion**: The total displacement from the starting point is **5 meters** in a direction that can be described as northeast, since it is a combination of east and north movements. ### Explanation of Other Options - **Option B (7 meters)**: This option might confuse distance with displacement. The total distance traveled is 4 meters east + 3 meters north = 7 meters, but this is not the displacement, which is the straight-line distance. - **Option C (3 meters)**: This option incorrectly assumes that the displacement is only the northward movement. Displacement considers both the east and north movements, not just one direction. - **Option D (4 meters)**: This option only considers the eastward movement and ignores the northward component. Displacement must account for both movements. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path traveled, while displacement is the shortest straight-line distance between two points. - Forgetting to use the Pythagorean theorem when dealing with right triangles formed by movements in perpendicular directions. ### 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 are in perpendicular directions. - The correct displacement in this scenario is 5 meters, calculated from the coordinates of the starting and ending points. - Always differentiate between total distance traveled and displacement to avoid confusion.