Subjects geometry

Miranda Path 87Fe97

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1. **State the problem:** Miranda starts at Point B facing north and wants to reach Point F. She makes a 1/4 turn clockwise, walks 4 squares east, makes another 1/4 turn clockwise, then walks 3 squares south. We need to find her final position relative to Point B and confirm she reaches Point F. 2. **Understand the turns and directions:** - Facing north initially. - A 1/4 turn clockwise from north points east. - After walking 4 squares east, another 1/4 turn clockwise from east points south. - Then she walks 3 squares south. 3. **Calculate the total displacement:** - First move: 4 squares east. - Second move: 3 squares south. 4. **Express displacement in coordinates:** Assuming Point B is at origin $(0,0)$, - Moving 4 squares east: $(+4,0)$ - Moving 3 squares south: $(0,-3)$ 5. **Add displacements:** $$ (0,0) + (4,0) + (0,-3) = (4,-3) $$ 6. **Conclusion:** Miranda ends at coordinates $(4,-3)$ relative to Point B, which corresponds to Point F on the grid. Therefore, Miranda successfully reaches Point F by following the described path.