Part A:
City Name: Gridville
Landmark Locations:
- Courthouse: (-2, 11)
- Electric Company: (-7, -4)
- School: (0, 7)
- Historic Mansion: (-14, 4)
- Post Office: (4, -5)
River Equation: y = 2x - 5
Main Highway Equation: 4x + 3y = 12
Tourist Center: Located at the intersection of 1st Street and the Main Highway, coordinates (3, 8).
Part B:
Planning 4 new roads parallel to 1st Street:
1. 2nd Street: y = 7
2. 3rd Street: y = 6
3. 4th Street: y = 5
4. 5th Street: y = 4
Part C:
Establishing 5 new roads perpendicular to 1st Street:
1. A Street: x = 3
2. B Street: x = 4
3. C Street: x = -1
4. D Street: x = -2
5. E Street: x = 2
Part D:
No bridges are needed for these new streets as they all intersect with 1st Street at ground level.
Part E:
Fire Station Location:
- Midpoint between the tourist center (3, 8) and the electric company (-7, -4):
- x = (3 - 7) / 2 = -2 / 2 = -1
- y = (8 - (-4)) / 2 = 12 / 2 = 6
- Fire Station location: (-1, 6)
Park Location:
- Midpoint between the school (0, 7) and the historic mansion (-14, 4):
- x = (0 - 14) / 2 = -14 / 2 = -7
- y = (7 + 4) / 2 = 11 / 2 = 5.5
- Park location: (-7, 5.5)
Part F:
Zoo Location:
- Ratio of its distance from the post office (4, -5) to the distance from the school (0, 7) is 1:3.
- Let the zoo's location be (x, y).
- Using the ratio, we have:
- (x - 4) / (x - 0) = 1/3
- Solve for x: 3(x - 4) = x
- 3x - 12 = x
- 2x = 12
- x = 6
- Now, find y using the equation of the river (y = 2x - 5):
- y = 2(6) - 5
- y = 12 - 5
- y = 7
- Zoo location: (6, 7)
Part G:
Choose 4 retail locations:
1. Home Improvement Store: (3, 7)
2. Grocery: (-1, 7)
3. Gas Station: (-7, 7)
4. Electronics Store: (-14, 7)
Restaurants:
1. Restaurant A: Located at the intersection of 2nd Street and 3rd Street, coordinates (3, 6).
2. Restaurant B: Located at the intersection of 4th Street and A Street, coordinates (-2, 5).