**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 jogger runs 3 kilometers east and then 4 kilometers north. - We can visualize this movement on a coordinate plane where the starting point is at the origin (0,0). - Moving 3 kilometers east places the jogger at the point (3,0). - Moving 4 kilometers north from (3,0) takes the jogger to the point (3,4). 3. **Using the Pythagorean Theorem**: - To find the displacement, we need to calculate the straight-line distance from the starting point (0,0) to the final point (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. - Here, the two sides of the triangle are: - The eastward distance: 3 kilometers - The northward distance: 4 kilometers - According to the Pythagorean theorem: \[ d^2 = a^2 + b^2 \] where \(d\) is the displacement, \(a\) is the eastward distance, and \(b\) is the northward distance. - Plugging in the values: \[ d^2 = 3^2 + 4^2 \] \[ d^2 = 9 + 16 \] \[ d^2 = 25 \] \[ d = \sqrt{25} = 5 \text{ kilometers} \] 4. **Conclusion**: The jogger's displacement from the starting point is 5 kilometers in a direction that can be determined using trigonometry (specifically, the angle can be found using the tangent function, but that is not necessary for this question). ### Why Other Options Are Incorrect - **Option B (7 kilometers)**: This option might confuse distance traveled with displacement. The jogger traveled a total distance of 3 km + 4 km = 7 km, but this is not the displacement, which is the straight-line distance from start to finish. - **Option C (1 kilometer)**: This option is incorrect as it does not represent any calculation related to the jogger's path. The jogger's movements do not lead to a displacement of 1 kilometer. - **Option D (12 kilometers)**: This option also misrepresents the situation. It could be mistakenly thought of as the total distance traveled, but again, it does not reflect the straight-line displacement. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path length, 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. ### 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 jogger's displacement in this case is 5 kilometers. - Always differentiate between total distance traveled and displacement.