Questions: Points: 0 or 1 The units of the subway map below are in miles. Suppose the routes between stations are straight. Station F, not shown on the map, is 10 miles west and 5 miles north of Station A. What is the approximate distance between Station E and Station F? The distance from Station E to Station F is approximately miles. (Round to the nearest tenth as needed.)

Solution Steps

From the graph, Station A is located at the coordinates (2, 3).

Station F is 10 miles west and 5 miles north of Station A.

• Moving 10 miles west from (2, 3) results in (2 - 10, 3) = (-8, 3).
• Moving 5 miles north from (-8, 3) results in (-8, 3 + 5) = (-8, 8).

From the graph, Station E is located at the coordinates (-4, -2).

Use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substitute the coordinates of Station E (-4, -2) and Station F (-8, 8): \[ \text{Distance} = \sqrt{(-8 - (-4))^2 + (8 - (-2))^2} \] \[ \text{Distance} = \sqrt{(-8 + 4)^2 + (8 + 2)^2} \] \[ \text{Distance} = \sqrt{(-4)^2 + (10)^2} \] \[ \text{Distance} = \sqrt{16 + 100} \] \[ \text{Distance} = \sqrt{116} \] \[ \text{Distance} \approx 10.8 \]

Final Answer