**Correct Option: A. 5 kilometers** ### 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 Problem**: - The hiker starts at a point (let's call it point O). - The hiker walks 3 kilometers east (let's call this point A). - Then, the hiker walks 4 kilometers north (let's call this point B). - We can visualize this as a right triangle where: - The horizontal leg (eastward) is 3 km. - The vertical leg (northward) is 4 km. 3. **Using the Pythagorean Theorem**: To find the displacement (the straight-line distance from the starting point O to the final point B), we can use the Pythagorean theorem, which states: \[ c^2 = a^2 + b^2 \] where: - \(c\) is the hypotenuse (the displacement), - \(a\) is one leg of the triangle (3 km), - \(b\) is the other leg of the triangle (4 km). 4. **Calculating the Displacement**: - Substitute the values into the formula: \[ c^2 = (3 \text{ km})^2 + (4 \text{ km})^2 \] \[ c^2 = 9 \text{ km}^2 + 16 \text{ km}^2 \] \[ c^2 = 25 \text{ km}^2 \] - Now, take the square root of both sides to find \(c\): \[ c = \sqrt{25 \text{ km}^2} = 5 \text{ km} \] 5. **Conclusion**: The hiker's displacement from the starting point is 5 kilometers in a direction that can be described as northeast, since it is a combination of east and north movements. ### Why Other Options Are Incorrect - **Option B (7 kilometers)**: This option might confuse distance traveled with displacement. The total distance the hiker walked is 3 km + 4 km = 7 km, but this is not the displacement, which is the straight-line distance. - **Option C (12 kilometers)**: This option is incorrect as it does not relate to any calculation of distance or displacement in this scenario. It may arise from misunderstanding the path taken. - **Option D (1 kilometer)**: This option is incorrect as it significantly underestimates the displacement. The hiker's movements create a right triangle, and the shortest distance (displacement) cannot be less than either leg of the triangle. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path traveled, while displacement is the shortest straight-line distance. - Misapplying the Pythagorean theorem: Ensure that you are using it correctly for right triangles, where the legs are perpendicular to each other. ### Revision Summary - Displacement is the shortest distance from the starting point to the final point, considering direction. - Use the Pythagorean theorem for right triangles to calculate displacement. - The hiker's displacement in this scenario is 5 kilometers. - Always differentiate between total distance traveled and displacement in physics problems.