Question

question 1
find the direct distance from the fire station to the hospital using the pythagorean theorem. show your work.

1. reflect on your creation.

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.

Explanation:

Step1: Determine the horizontal and vertical distances

Assume the coordinates of the Fire Station are \((x_1,y_1)\) and of the Hospital are \((x_2,y_2)\). Count the number of squares horizontally (\(a\)) and vertically (\(b\)) between them. If each square is \(100\) meters, then the horizontal distance \(a = 5\times100 = 500\) meters and the vertical distance \(b= 2\times100=200\) meters.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the direct distance. Substitute \(a = 500\) and \(b = 200\) into the formula: \(c=\sqrt{500^{2}+200^{2}}=\sqrt{250000 + 40000}=\sqrt{290000}\approx538.52\) meters.

Answer:

The direct distance from the Fire Station to the Hospital is approximately \(538.52\) meters.