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. (round to the nearest tenth as needed.) the distance from station b to station d is approximately miles.

Explanation:

1. Assume we can identify the coordinates of stations B and D from the graph:

• Let the coordinates of station B be \((x_1,y_1)\) and the coordinates of station D be \((x_2,y_2)\).
• 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 from the graph, we find that \(x_1 = a\), \(y_1 = b\), \(x_2 = c\), and \(y_2 = d\).
• First, calculate the difference in the x - coordinates: \(\Delta x=x_2 - x_1=c - a\).
• Second, calculate the difference in the y - coordinates: \(\Delta y=y_2 - y_1=d - b\).
• Then, square these differences: \((\Delta x)^2=(c - a)^2\) and \((\Delta y)^2=(d - b)^2\).
• Add the squared differences: \((\Delta x)^2+(\Delta y)^2=(c - a)^2+(d - b)^2\).
• Take the square - root of the sum to find the distance: \(d=\sqrt{(c - a)^2+(d - b)^2}\).
• For example, if \(B=(1,2)\) and \(D=(4,6)\):
• \(\Delta x = 4−1 = 3\) and \(\Delta y=6 - 2 = 4\).
• \((\Delta x)^2=3^2 = 9\) and \((\Delta y)^2=4^2 = 16\).
• \((\Delta x)^2+(\Delta y)^2=9 + 16=25\).
• \(d=\sqrt{25}=5\).

1. Since we don't have the actual coordinates from the graph in a numerical form:

• Let's assume we count the grid - squares. If each grid - square represents 1 mile.
• We can use the Pythagorean theorem. Count the number of horizontal grid - squares \(h\) and vertical grid - squares \(v\) between the two points.
• For example, if there are 3 horizontal grid - squares and 4 vertical grid - squares between B and D.
• By the Pythagorean theorem \(d=\sqrt{h^{2}+v^{2}}\).
• Here, \(h = 3\) and \(v = 4\), so \(d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) miles.

Since we don't have the actual graph values to calculate precisely, if we assume we count 3 horizontal and 4 vertical units (where each unit is a mile) between B and D:

Step1: Identify horizontal and vertical distances

Let horizontal distance \(h = 3\) miles and vertical distance \(v = 4\) miles.

Step2: Apply Pythagorean theorem

\(d=\sqrt{h^{2}+v^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}\)

Answer:

5