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. (round to the nearest)

Explanation:

Step1: Identify coordinates

Assume the grid - based coordinates of station J and K. Let's say the coordinates of station J are $(x_1,y_1)$ and of station K are $(x_2,y_2)$. From the graph, if we consider the grid lines as unit intervals, assume J=(1, - 3) and K=(4, - 1).

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 $x_1 = 1,y_1=-3,x_2 = 4,y_2=-1$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(4 - 1)^2+(-1+3)^2}\\ &=\sqrt{3^2 + 2^2}\\ &=\sqrt{9 + 4}\\ &=\sqrt{13}\approx 3.6 \end{align*}$$

\]

Answer:

3.6