Question

2. (12 points) You are managing a squad of fire department helicopters. There is a fire that needs tobe put out, and several helicopters in the area could help. On the gridded map below, each unit is 1mile:

Answer 1

For A.

First, we need to calculate the distance between Helicopter 1 and the fire

Fire (-3,-5)

Helicopter 1 (1,4)

the formula of the distance between 2 points is

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

where

(-3,-5)=(x1,y1)

(1,4)=(x2,y2)

we substitute the values

`\begin{gathered} d=\sqrt[]{(1+3)^2+(4+5)^2} \\ d=\sqrt[]{4^2+9^2} \\ d=9.85\text{ miles} \end{gathered}`

We didn't send helicopter 1 because it is a located 9.85 miles from the fire and it is only useful if it is within 9 miles so we don't send it

For B.

we need to calculate the distance between the fire and Helicopters 2 and 3

Helicopter 2 (-2,3)

Helicopter 3(4,-2)

Distance between helicopter 2 and the fire

(-2,3)=(x1,y1)

(-3,-5)=(x2,y2)

`\begin{gathered} d=\sqrt[]{(-3+2)^2+(-5-3)} \\ d=\sqrt[]{65} \\ d=8.06 \end{gathered}`

Distance between helicopter 3 and the fire

(4,-2)=(x1,y1)

(-3,-5)=(x2,y2)

`\begin{gathered} d=\sqrt[]{(-3-4)^2+(-5+2)^2} \\ d=\sqrt[]{58} \\ d=7.6 \end{gathered}`

as we can see the distance between the fire and helicopter 2 is bigger than 8, the distance between helicopter 3 and the fire is less than 8 therefore we will send the Helicopter 3