the units of the subway map below are in miles. suppose the routes between stations are straight. find the…

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 miles. (round to the nearest tenth as needed.)

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 miles. (round to the nearest tenth as needed.)

Answer

  1. First, assume the coordinates of Station (J) and Station (K) are ((x_1,y_1)) and ((x_2,y_2)) respectively. If we can read the coordinates from the graph (let's say (J(x_1,y_1)) and (K(x_2,y_2))), we use the distance - formula (d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}).
    • For example, if (J(2,1)) and (K(5,4)):
      • Calculate ((x_2 - x_1)) and ((y_2 - y_1)):
        • (x_2 - x_1=5 - 2 = 3).
        • (y_2 - y_1=4 - 1 = 3).
      • Then use the distance formula:
        • (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{3^2 + 3^2}=\sqrt{9 + 9}=\sqrt{18}).
        • Simplify (\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\approx3\times1.414 = 4.242\approx4.2) (rounded to the nearest tenth).

Answer:

<The value obtained after applying the distance - formula and rounding to the nearest tenth>

Explanation:

Step1: Identify coordinates

<Read coordinates of (J) and (K) from the graph>

Step2: Calculate differences

<Find (x_2 - x_1) and (y_2 - y_1)>

Step3: Apply distance formula

<Substitute into (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2})>

Step4: Simplify and round

<Simplify the result and round to nearest tenth>