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 b and d.

Explanation:

1. Explanation:

• First, assume the coordinates of station B and station D. Let's assume the coordinates of station B are \((x_1,y_1)\) and of station D are \((x_2,y_2)\) by looking at the grid - the coordinates of a point in a Cartesian plane.
• Then, use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• Suppose station B has coordinates \((- 6,1)\) and station D has coordinates \((0,-2)\) (by observing the grid).
• Calculate the difference in \(x\) - coordinates: \(x_2 - x_1=0-(-6)=6\).
• Calculate the difference in \(y\) - coordinates: \(y_2 - y_1=-2 - 1=-3\).
• Substitute into the distance formula:
• \(d=\sqrt{(6)^2+(-3)^2}=\sqrt{36 + 9}=\sqrt{45}\).
• Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx3\times2.24 = 6.72\) (since \(\sqrt{5}\approx2.24\)).

1. Answer:

The approximate distance between stations B and D is \(6.72\) miles.

Answer:

1. Explanation:

• First, assume the coordinates of station B and station D. Let's assume the coordinates of station B are \((x_1,y_1)\) and of station D are \((x_2,y_2)\) by looking at the grid - the coordinates of a point in a Cartesian plane.
• Then, use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• Suppose station B has coordinates \((- 6,1)\) and station D has coordinates \((0,-2)\) (by observing the grid).
• Calculate the difference in \(x\) - coordinates: \(x_2 - x_1=0-(-6)=6\).
• Calculate the difference in \(y\) - coordinates: \(y_2 - y_1=-2 - 1=-3\).
• Substitute into the distance formula:
• \(d=\sqrt{(6)^2+(-3)^2}=\sqrt{36 + 9}=\sqrt{45}\).
• Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx3\times2.24 = 6.72\) (since \(\sqrt{5}\approx2.24\)).

1. Answer:

The approximate distance between stations B and D is \(6.72\) miles.