1. **Problem Statement:** Moira walked 3.5 km west and then 4.5 km north from her house. We need to find the straight-line distance from her current position back to her house. 2. **Understanding the problem:** The path forms a right-angled triangle where: - One leg is 3.5 km (westward distance) - The other leg is 4.5 km (northward distance) - The hypotenuse is the straight-line distance from Moira to her house 3. **Formula used:** To find the hypotenuse $c$ of a right triangle with legs $a$ and $b$, use the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ 4. **Applying the formula:** $$a = 3.5, \quad b = 4.5$$ $$c = \sqrt{3.5^2 + 4.5^2} = \sqrt{12.25 + 20.25} = \sqrt{32.5}$$ 5. **Calculating the value:** $$c \approx 5.7$$ 6. **Conclusion:** The straight-line distance between Moira and her house is approximately 5.7 km. This distance is the hypotenuse of the right triangle formed by her westward and northward walks.