Question

emergency response planning
you are helping your city plan emergency routes in a new neighborhood. the neighborhood is on a coordinate grid where each square represents 100 meters. emergency vehicles can travel on streets (grid lines) or cut diagonally through parks when responding to emergencies.
which is closer to the new school: the hospital or the police station? calculate both distances to support your answer.

Explanation:

Step1: Determine coordinates

Assume the school is at \((9,2)\), hospital at \((8,5)\), police station at \((5,7)\).

Step2: Calculate distance using distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For hospital - school:
\(d_{hospital}=\sqrt{(9 - 8)^2+(2 - 5)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16\) (in grid units). In meters: \(3.16\times100 = 316\) meters.
For police station - school:
\(d_{police}=\sqrt{(9 - 5)^2+(2 - 7)^2}=\sqrt{16 + 25}=\sqrt{41}\approx6.40\) (in grid units). In meters: \(6.40\times100=640\) meters.

Answer:

The hospital is closer to the new school. The distance from the hospital to the school is approximately \(316\) meters and from the police station to the school is approximately \(640\) meters.