To determine the total displacement of a person who walks 3 meters east and then 4 meters north, we can visualize the situation and apply the Pythagorean theorem. Let's break this down step-by-step. ### Step 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 how much ground is covered, regardless of direction. ### Step 2: Visualizing the Movement 1. **Starting Point**: Imagine a coordinate system where the starting point is at the origin (0, 0). 2. **First Movement**: The person walks 3 meters east. This can be represented as moving from (0, 0) to (3, 0). 3. **Second Movement**: Then, the person walks 4 meters north. This movement takes them from (3, 0) to (3, 4). ### Step 3: Finding the Displacement Now, we need to find the straight-line distance from the starting point (0, 0) to the final position (3, 4). This forms a right triangle where: - One leg (eastward movement) is 3 meters. - The other leg (northward movement) is 4 meters. ### Step 4: Applying the Pythagorean Theorem To find the hypotenuse (which represents the displacement), we can use the Pythagorean theorem, which states: \[ c^2 = a^2 + b^2 \] where: - \(c\) is the hypotenuse (displacement), - \(a\) is one leg (3 meters), - \(b\) is the other leg (4 meters). Substituting the values: \[ c^2 = 3^2 + 4^2 \] \[ c^2 = 9 + 16 \] \[ c^2 = 25 \] Taking the square root of both sides gives: \[ c = \sqrt{25} = 5 \text{ meters} \] ### Conclusion The total displacement from the starting point is **5 meters**. Therefore, the correct option is **C**. ### Step 5: Analyzing Other Options - **Option A (3 meters)**: This option only considers the eastward movement and ignores the northward movement. It does not represent the total displacement. - **Option B (4 meters)**: This option only considers the northward movement and ignores the eastward movement. Like option A, it does not represent the total displacement. - **Option D (7 meters)**: This option incorrectly adds the two movements (3 meters + 4 meters) as if they were in a straight line. However, displacement is not simply the sum of the distances traveled in different 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 at right angles. - In this case, the movements create a right triangle with legs of 3 meters and 4 meters. - The total displacement calculated is 5 meters, making option C the correct answer.