Question

1. you are helping to create a map of a town.

a. use the coordinate plane to create a map of a town that meets the following requirements.
each location must be represented on the map. do not extend the town boundaries. the
point for each location must be plotted where two grid lines intersect.
each square on the grid represents 1 block. each line on the grid represents a street.
plot a point to represent each location on the map. label each point.

• the fire station is located at (5, 0).
• the fire station is directly east of town hall.
• the police station is 6 blocks north of the fire station.
• the school is northwest of town hall.
• the distance from the school to the police station is equal to |−3| + |5| blocks.
• the ice cream shop is 5 blocks west and 2 blocks south of town hall.
• the museum is within 5 blocks of town hall.
• the library is no more than 3 blocks from the museum and no more than 5 blocks from

the school.

Explanation:

Step1: Find Town Hall coordinates

Fire station is at $(5,0)$, east of Town Hall, so Town Hall is west (subtract x-value). Let Town Hall = $(x,0)$. Since east means higher x, Town Hall is $(0,0)$ (fire station is 5 blocks east: $5-0=5$ blocks, matches grid).

Step2: Find Police Station coordinates

6 blocks north of fire station $(5,0)$: add 6 to y-value.
Expression: $(5, 0+6)=(5,6)$

Step3: Calculate school-police distance

Compute $|-3| + |5| = 3+5=8$ blocks.

Step4: Find School coordinates

Northwest of Town Hall $(0,0)$: $x<0, y>0$. Distance to police $(5,6)$ is 8. Use distance formula: $\sqrt{(x-5)^2 + (y-6)^2}=8$. Test $(-3,5)$: $\sqrt{(-3-5)^2 + (5-6)^2}=\sqrt{64+1}=\sqrt{65}
eq8$. Test $(-4,4)$: $\sqrt{(-4-5)^2 + (4-6)^2}=\sqrt{81+4}=\sqrt{85}
eq8$. Test $(-3,6)$: $\sqrt{(-3-5)^2 + (6-6)^2}=\sqrt{64}=8$. This works, and $(-3,6)$ is northwest of $(0,0)$.

Step5: Find Ice Cream Shop coordinates

5 blocks west (subtract 5 from x) and 2 blocks south (subtract 2 from y) of Town Hall $(0,0)$.
Expression: $(0-5, 0-2)=(-5,-2)$

Step6: Choose Museum coordinates

Within 5 blocks of Town Hall $(0,0)$: e.g., $(2,3)$ (distance $\sqrt{2^2+3^2}=\sqrt{13}<5$)

Step7: Choose Library coordinates

No more than 3 blocks from Museum $(2,3)$ and ≤5 blocks from School $(-3,6)$. E.g., $(0,4)$: distance to museum $\sqrt{(0-2)^2+(4-3)^2}=\sqrt{5}<3$, distance to school $\sqrt{(0+3)^2+(4-6)^2}=\sqrt{13}<5$

Answer:

Plotted points (on the coordinate grid):

• Town Hall: $(0,0)$
• Fire Station: $(5,0)$
• Police Station: $(5,6)$
• School: $(-3,6)$
• Ice Cream Shop: $(-5,-2)$
• Museum: $(2,3)$ (example valid point)
• Library: $(0,4)$ (example valid point)

(Note: Museum and Library have multiple valid positions that meet the distance requirements; the above are just one valid set.)