Chapter 8.1, Problem 52PS

Solution

To find: the straight-line distance between Li’s home and her office.

The straight distance between Li’s home and her office is $6.4\text{ miles}\text{.}$

Given:

It is given that Li must drive around a lake. She drives $2\text{ miles}$ north, then $5\text{ miles}$ east and the $4\text{ miles}$ south.

Calculation:

Let the Li’s home at the origin. She starts her journey from origin and the trajectory that she followed for her office is shown below:

  

Now, calculating the straight line distance between her home and office using the distance formula as:

  $BD=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

where,

  $B=\left(0,2\right)\text{ and }D=\left(5,-2\right)$

So, the distance from her home to her office is:

  $\begin{array}{l}BD=\sqrt{{\left(5-0\right)}^2+{\left(-2-2\right)}^2}\\ BD=\sqrt{25+16}\\ BD=\sqrt{41}\\ BD=6.4\end{array}$

Hence, the straight-line distance between Li’s home and office is $6.4\text{ miles}\text{.}$