To determine the hiker's displacement from point A to point C, we need to understand what displacement means and how to calculate it using the information given. ### 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 Path**: - The hiker starts at point A and walks 3 km east to point B. Then, from point B, the hiker walks 4 km north to point C. - If we visualize this on a coordinate system, we can place point A at the origin (0, 0). - Moving 3 km east to point B would place point B at (3, 0). - From point B, moving 4 km north to point C would place point C at (3, 4). 3. **Calculating Displacement**: - To find the displacement from point A (0, 0) to point C (3, 4), we can use the Pythagorean theorem. The displacement forms a right triangle where: - The horizontal leg (eastward movement) is 3 km. - The vertical leg (northward movement) is 4 km. - According to the Pythagorean theorem: \[ d = \sqrt{x^2 + y^2} \] where \(x\) is the horizontal distance and \(y\) is the vertical distance. - Plugging in the values: \[ d = \sqrt{(3 \text{ km})^2 + (4 \text{ km})^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km} \] 4. **Final Answer**: - Therefore, the hiker's displacement from point A to point C is **5 km**. ### Why Other Options Are Incorrect - **Option A (3 km)**: This option represents only the distance traveled east from A to B. It does not account for the northward movement to point C, so it is not the correct displacement. - **Option B (4 km)**: This option represents only the distance traveled north from B to C. Similar to option A, it does not consider the total displacement from A to C, making it incorrect. - **Option D (7 km)**: This option incorrectly adds the distances traveled (3 km + 4 km) instead of calculating the straight-line distance (displacement) from A to C. This is a common misconception where students confuse total distance with displacement. ### Common Pitfalls - Confusing distance with displacement: Remember that distance is the total path length, while displacement is the straight-line distance between two points. - Forgetting to use the Pythagorean theorem for right triangles: Always check if the movements form a right triangle when calculating displacement. ### Revision Summary - Displacement is the shortest distance from the starting point to the endpoint, including direction. - Use the Pythagorean theorem to calculate displacement when movements are perpendicular. - The correct displacement from point A to point C is 5 km. - Be careful not to confuse total distance traveled with displacement.