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:

• Step 1: Identify the coordinates of points J and K
• Assume the coordinates of point J are \((x_1,y_1)\) and of point K are \((x_2,y_2)\) by looking at the grid - based on the position of the stations on the coordinate - like system of the subway map. Let's say \(J=(x_1,y_1)\) and \(K=(x_2,y_2)\) where we can read the values from the grid. For example, if \(J=(2,6)\) and \(K=(0,2)\) (values are assumed for illustration purposes as the actual values are not clearly readable in the provided image).
• Step 2: Apply the 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 the values of \(x_1,y_1,x_2,y_2\) into the formula. If \(x_1 = 2,y_1 = 6,x_2 = 0,y_2 = 2\), then \(d=\sqrt{(0 - 2)^2+(2 - 6)^2}=\sqrt{(- 2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.5\) (rounded to the nearest tenth).

1. Answer:

• The answer depends on the actual coordinates of points J and K read from the map. But following the above - described process, if we assume the correct coordinates and calculate, we get the distance value. For example, if the calculated value is \(d\approx4.5\) (after substituting the correct coordinates into the distance formula), the answer is \(4.5\) (rounded to the nearest tenth).

Answer:

1. Explanation:

• Step 1: Identify the coordinates of points J and K
• Assume the coordinates of point J are \((x_1,y_1)\) and of point K are \((x_2,y_2)\) by looking at the grid - based on the position of the stations on the coordinate - like system of the subway map. Let's say \(J=(x_1,y_1)\) and \(K=(x_2,y_2)\) where we can read the values from the grid. For example, if \(J=(2,6)\) and \(K=(0,2)\) (values are assumed for illustration purposes as the actual values are not clearly readable in the provided image).
• Step 2: Apply the 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 the values of \(x_1,y_1,x_2,y_2\) into the formula. If \(x_1 = 2,y_1 = 6,x_2 = 0,y_2 = 2\), then \(d=\sqrt{(0 - 2)^2+(2 - 6)^2}=\sqrt{(- 2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.5\) (rounded to the nearest tenth).

1. Answer:

• The answer depends on the actual coordinates of points J and K read from the map. But following the above - described process, if we assume the correct coordinates and calculate, we get the distance value. For example, if the calculated value is \(d\approx4.5\) (after substituting the correct coordinates into the distance formula), the answer is \(4.5\) (rounded to the nearest tenth).