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

Explanation:

Step1: Find the coordinates of points J and K

Assume the coordinates of point K are \((- 10,2)\) and of point J are \((14,-1)\) (by observing the grid).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Let \((x_1,y_1)=(-10,2)\) and \((x_2,y_2)=(14,-1)\). Then \(x_2 - x_1=14-(-10)=24\) and \(y_2 - y_1=-1 - 2=-3\).

Step3: Calculate the distance

\(d=\sqrt{(24)^2+(-3)^2}=\sqrt{576 + 9}=\sqrt{585}\approx24.2\)

Answer:

\(24.2\)