Question

planning a City O N A C O O R D I N A T E. G R I D You have established a city that is just beginning to grow. You will need to put a plan into place so your city will grow successfully and efficiently. Decide on a name for your city: ____________________________________ Part A: Locate the following landmarks on a coordinate plane. (If you are creating your own, usegraph paper, and draw the origin in the middle. The grid should extend 20 units in all directions.) Each unit on your paper will represent 0.1 of a mile. As you add features to your city throughout the activity, be sure to mark and label each one on your grid. Some landmarks are established in your city and would be very difficult to relocate. Locate and placethese landmarks on your grid with a dot and label: • Courthouse (-2, 11) • Electric Company (-7, -4) • School (0, 7) • Historic Mansion (-14, 4) • Post Office (4, -5) • A river runs through your city following the equation y= 2x − 5. • The main highway runs through your city following the equation 4x + 3y = 12 • The only other paved road (1st Street) currently runs from the courthouse to the electric company. Your city would like to attract tourists, so you will need a tourist center at the point where the main highway and 1st Street intersect. Where will the tourist center be located? __(3,8)_______ Part B: Plan 4 new roads to run parallel to 1st Street. You should pick the locations thoughtfully, planning for where you think you will have traffic. Write the equations for these roads. Street name Equation Part C: Now establish 5 additional roads to run perpendicular to 1st Street. Street name Equation Part D: Will you need any bridges on these new streets? What coordinates will require bridges? Part E: The fire station should be located at the midpoint between the tourist center and the electric company. Show the calculations to find its location. Label it on the grid. (-5, 2) A park is located at the midpoint between the school and the historic mansion. Show the calculations to find its location. Label it on the grid. (-7, 5.5) Part F: The zoo is located between the post office and school, but not at the midpoint. The ratio of its distance from the post office to the distance from the school is 1:3. Show the calculations to find its location. Label it on the grid. (3, -2) Part G: The following retail locations have submitted applications to build stores in your city. Choose 4 of the following to locate in your city. Pick a location for each one at the intersection of 2 streets. Home Improvement Store Clothing Store Grocery Pharmacy Gas Station Electronics Store Convenience Market Cell Phone Retailer Organic Grocery Bakery Wholesale Club Store Discount Clothing Store Toy Store Art Gallery Donut Shop R e t a i l e r c o o r d i n a t e s 2 restaurants will also locate in your city. What are the restaurants and where are they?

Answer 1

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).

Answer 2

The tourist center at coordinates (3, 8). They should plan four new roads parallel to 1st Street using slope-intercept form equations. Five additional roads perpendicular to 1st Street should be established using the x = c form equation. Bridges will be needed where the new roads intersect with the river. The fire station and park can be located at the midpoints between specific landmarks. The zoo can be located using a ratio calculation. Four retail locations can be located at the intersections of two streets.

Step-by-step explanation:

The tourist center will be located at the intersection of the main highway and 1st Street, which is at coordinates (3, 8).

For Part B, you can plan four new roads parallel to 1st Street by using equations in the form y = mx + b, where m is the slope of the road and b is the y-intercept. The locations can be chosen thoughtfully, considering areas where traffic is expected. You can label each road with a name and its corresponding equation.

For Part C, you can establish five additional roads perpendicular to 1st Street using equations in the form x = c, where c is a constant value. Each road should have a name and its corresponding equation.

In Part D, bridges will be needed when a road crosses over the river or any other water bodies. You can determine the coordinates that will require bridges by finding the intersections of the new roads with the equation of the river.

In Part E, the fire station should be located at the midpoint between the tourist center and the electric company, which is at coordinates (-5, 2). The park should be located at the midpoint between the school and the historic mansion, which is at coordinates (-7, 5.5).

In Part F, to find the location of the zoo, you can use ratios. The distance from the post office to the zoo is one-third of the distance from the school to the zoo. By calculating the coordinates using the given ratio, the location of the zoo is (3, -2).

For Part G, you can choose four of the given retail locations and locate them at the intersections of two streets. Each intersection should have coordinates.