Question

your itinerary contains a grid map of washington d.c., with each unit on the grid representing 0.125 miles. if arlington cemetery is located at (6, - 2) and the pentagon is located at (-13,4), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? round your answer to two decimal places if necessary.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(6,-2)$ and $(x_2,y_2)=(-13,4)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-13 - 6=-19$ and $y_2 - y_1=4-( - 2)=6$.

Step3: Square the differences

$(x_2 - x_1)^2=(-19)^2 = 361$ and $(y_2 - y_1)^2=6^2 = 36$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=361 + 36=397$.

Step5: Calculate distance in grid units

The distance $d$ in grid units is $d=\sqrt{397}\approx19.924858$.

Step6: Convert to miles

Since each grid - unit represents $0.125$ miles, the distance in miles is $19.924858\times0.125 = 2.49060725\approx2.49$ miles.

Answer:

$2.49$