Chapter 8.3, Problem 38E

To determine

The distance between the school and the mall.

Answer to Problem 38E

  $d=3.5\text{miles}$

Explanation of Solution

Given:

One block = 0.1 mile.

School is 20 blocks east and 12 blocks south of the house.

Mall is 10 blocks north and 7 blocks west of the house.

Calculation:

Let the house is at origin. The coordinates of mall and house will be:

  $\begin{array}{l}M=\left(-7,10\right)\\ S=\left(20,-12\right)\end{array}$

That is,

  

Using distance formula:

  $\begin{array}{l}SM=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ SM=\sqrt{{\left(-7-20\right)}^2+{\left(10-\left(-12\right)\right)}^2}\\ SM=\sqrt{729+484}\\ SM=\sqrt{1213}\\ SM=34.82\text{blocks}\end{array}$

Therefore,

  $\begin{array}{l}d=\frac{34.82}{1}\times \frac{0.1\text{mile}}{1\text{block}}\\ d=3.5\text{miles}\end{array}$