Chapter 8.1, Problem 49PS

Solution

To find: Use the information given to find the distance a medical evacuation (“medevac”) helicopter would have to fly to Memorial Medical Center from each location. Each unit on the map represents 1 mile, and the letters N, S, E, and W indicate direction.

Hence, the distance between Memorial Medical Center and University of Illinois is 6.01 miles.

Given: the location University of Illinois

Concept Used:

distance formula is given by $d=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}$

Calculation: Coordinates of Memorial Medical Center is $00.5N\Rightarrow \left(0,0.5\right)$

And Coordinates University of Illinois is $2.2E5.1S\Rightarrow \left(2.2,-5.1\right)$

Finding the distance between Memorial Medical Center and University of Illinois:

  $\begin{array}{c}d=\sqrt{{\left(2.2-0\right)}^2+{\left(-5.1-0.5\right)}^2}\\ d=\sqrt{{\left(2.2\right)}^2+{\left(-5.6\right)}^2}\\ d=\sqrt{4.84+31.36}\\ d=\sqrt{36.2}\\ d=6.01664358\\ d\approx 6.01\text{ units}\\ d\approx 6.01\text{ miles}\end{array}$

Conclusion:

Hence, the distance between Memorial Medical Center and University of Illinois is 6.01 miles.