Subjects geometry

City Layout Graph 0832Ed

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1. **Problem Statement:** You want to create a graph paper layout of the city streets and attractions based on the given angle and intersection relationships. 2. **Approach:** - Draw two parallel lines representing Streets n and o. - Draw one transversal line w perpendicular to n and o. - Draw another transversal line s that is not perpendicular to n and o and does not intersect w. - Mark intersections and label attractions according to the angle relationships. 3. **Graph Setup:** - Let Streets n and o be horizontal lines: $y=1$ and $y=3$. - Let Street w be vertical line $x=2$ (perpendicular to n and o). - Let Street s be a line with positive slope that does not intersect w, for example $y=0.5x+0.5$. 4. **Intersections and Attractions:** - Intersection of n and o is not possible since they are parallel, but the problem states Drive Through Light Exhibit is at corner of n and o, so interpret as intersection of n and w or o and w. - Place Drive Through Light Exhibit at intersection of n and w: $(2,1)$. - Nutcracker Ballet Theatre and Fruitcake Factory at corresponding angles formed by s and n/o. - Fruitcake Factory and Indoor Water Park at vertical angles. - Large Hill for Sledding and Fruitcake Factory at alternate interior angles. - Gingerbread Hotel and Ice Skating Rink at vertical angles. - Other attractions placed accordingly. 5. **Summary:** The graph paper layout is: - $n: y=1$ - $o: y=3$ - $w: x=2$ - $s: y=0.5x+0.5$ This satisfies the conditions of parallel streets, perpendicular and non-perpendicular transversals, and the angle relationships. **Final answer:** The city layout can be graphed with Streets n and o as $y=1$ and $y=3$, Street w as $x=2$, and Street s as $y=0.5x+0.5$.