To determine the total displacement of the hiker from the starting point to the final position, we need to analyze the situation step by step. ### Step 1: Understanding Displacement Displacement is defined as the shortest straight-line distance from the initial position to the final position, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. ### Step 2: Analyzing the Hiker's Path The hiker walks: - 3 km east - 4 km north We can visualize this movement on a coordinate system: - Starting point (0, 0) - After walking 3 km east, the hiker is at (3, 0). - After walking 4 km north, the hiker is at (3, 4). ### Step 3: Calculating the Displacement To find the displacement, we can use the Pythagorean theorem. The displacement forms a right triangle where: - One leg (eastward movement) = 3 km - The other leg (northward movement) = 4 km According to the Pythagorean theorem: \[ d = \sqrt{x^2 + y^2} \] where \(d\) is the displacement, \(x\) is the distance east, and \(y\) is the distance north. Substituting the values: \[ d = \sqrt{(3 \text{ km})^2 + (4 \text{ km})^2} \] \[ d = \sqrt{9 \text{ km}^2 + 16 \text{ km}^2} \] \[ d = \sqrt{25 \text{ km}^2} \] \[ d = 5 \text{ km} \] ### Step 4: Conclusion The total displacement from the starting point to the final position of the hiker is **5 km**. ### Step 5: Evaluating the Options Now, let's evaluate the provided options: - **A. 5 km** - This is the correct answer, as calculated above. - **B. 7 km** - This option is incorrect because it does not represent the shortest distance between the starting and ending points. - **C. 10 km** - This option is incorrect as it suggests a longer distance than the actual displacement. - **D. 12 km** - This option is also incorrect, as it is significantly greater than the calculated displacement. ### Common Pitfalls - **Confusing distance with displacement**: Distance is the total path length traveled, while displacement is the straight-line distance from start to finish. - **Forgetting to use the Pythagorean theorem**: When dealing with right triangles, always remember to apply this theorem to find the resultant displacement. ### Revision Summary - Displacement is the shortest distance from the starting point to the final position. - Use the Pythagorean theorem to calculate displacement in right triangles. - The hiker's path forms a right triangle with legs of 3 km and 4 km. - The correct displacement is 5 km, which is option A.