Step 1: Identify the components of the displacement. The girl walks 100 m due East and then 100 m due North. These two movements are perpendicular to each other. Let the eastward displacement be $\Delta x = 100 \text{ m}$. Let the northward displacement be $\Delta y = 100 \text{ m}$. Step 2: Apply the Pythagorean theorem to find the magnitude of the resultant displacement. The displacement is the straight-line distance from the starting point to the final point, which forms the hypotenuse of a right-angled triangle. Let $d$ be the magnitude of the displacement. $$d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$$ Step 3: Substitute the values and calculate. $$d = \sqrt{(100 \text{ m})^2 + (100 \text{ m})^2}$$ $$d = \sqrt{10000 \text{ m}^2 + 10000 \text{ m}^2}$$ $$d = \sqrt{20000 \text{ m}^2}$$ $$d = \sqrt{10000 \times 2} \text{ m}$$ $$d = 100 \sqrt{2} \text{ m}$$ Using the approximation $\sqrt{2} \approx 1.414$: $$d \approx 100 \times 1.414 \text{ m}$$ $$d \approx 141.4 \text{ m}$$ Step 4: Compare the calculated displacement with the given options. The calculated displacement is approximately $141.4 \text{ m}$. The given options are: A. 100 B. 150 C. 200 D. 250 The closest option to $141.4 \text{ m}$ is $150 \text{ m}$. The final answer is $\boxed{\text{B. 150}}$. Send me the next one 📸