Subjects geometry

Direction Movement

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1. **Problem Statement:** Buchi starts from home and moves 8 km south, then 5 km east, then 3.5 km north, and finally 5 km west. We need to find the direction in which she is moving from her starting point. 2. **Understanding the Movement:** We can represent Buchi's movements on a Cartesian plane where north is positive y, south is negative y, east is positive x, and west is negative x. 3. **Calculate Final Coordinates:** - Initial position: $(0,0)$ - After moving 8 km south: $(0, -8)$ - After moving 5 km east: $(5, -8)$ - After moving 3.5 km north: $(5, -8 + 3.5) = (5, -4.5)$ - After moving 5 km west: $(5 - 5, -4.5) = (0, -4.5)$ 4. **Interpretation:** The final position is $(0, -4.5)$, which means Buchi is 4.5 km south of her starting point. 5. **Conclusion:** Buchi is moving directly south from her original location. **Final answer:** Buchi is moving **south**.