Question

the units of the subway map below are in miles. suppose the routes between stations are straight. find the approximate distance a passenger would travel between stations j and k. the distance from station j to station k is approximately (round to the nearest tenth as needed.)

Explanation:

Step1: Assume coordinates

Let's assume the coordinates of Station J are $(x_1,y_1)$ and of Station K are $(x_2,y_2)$ from the grid - based map. If we consider the grid as a coordinate - plane, and count the grid squares. Suppose Station J has coordinates $(1,3)$ and Station K has coordinates $(- 1,-2)$.

Step2: Apply distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1 = 1,y_1 = 3,x_2=-1,y_2 = - 2$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(-1 - 1)^2+(-2 - 3)^2}\\ &=\sqrt{(-2)^2+(-5)^2}\\ &=\sqrt{4 + 25}\\ &=\sqrt{29}\approx5.4 \end{align*}$$

\]

Answer:

5.4