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

Explanation:

1. Explanation:

• First, assume the coordinates of Station J and Station K. Let the coordinates of Station J be \((x_1,y_1)\) and of Station K be \((x_2,y_2)\) based on the grid - the distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a coordinate plane is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• Suppose Station J has coordinates \((x_1,y_1)=( - 2,-3)\) and Station K has coordinates \((x_2,y_2)=(3,1)\).
• Calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=3-( - 2)=3 + 2 = 5\).
• \(y_2 - y_1=1-( - 3)=1 + 3 = 4\).
• Then, use the distance formula:
• \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{5^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\).

1. Answer:

• \(\sqrt{41}\approx6.4\) (rounded to the nearest tenth). So the answer is \(6.4\).

Step1: Determine the distance formula

Use \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for two - point distance.

Step2: Find the differences in coordinates

\(x_2 - x_1=3-( - 2)=5\), \(y_2 - y_1=1-( - 3)=4\).

Step3: Calculate the distance

\(d=\sqrt{5^2+4^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4\).

Answer:

\(6.4\)