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The question asks for the approximate distance between Station E and Station G on a subway map, where Station G is not shown but is described as being 4 miles east and 6 miles south of Station A.

### Steps to solve:
1. **Coordinates of Station A and G:**
   - Station A is located at the origin (0, 0) based on the grid.
   - Station G is 4 miles east (positive x-direction) and 6 miles south (negative y-direction) of Station A. Thus, the coordinates of Station G are \( (4, -6) \).

2. **Coordinates of Station E:**
   - From the graph, Station E appears to be located at the point \( (-4, 2) \).

3. **Calculate the distance between Stations E and G:**
   The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the distance formula:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Plugging in the coordinates of Station E \( (-4, 2) \) and Station G \( (4, -6) \):
   \[
   d = \sqrt{(4 - (-4))^2 + (-6 - 2)^2} = \sqrt{(4 + 4)^2 + (-6 - 2)^2} = \sqrt{8^2 + (-8)^2} = \sqrt{64 + 64} = \sqrt{128}
   \]
   \[
   d \approx 11.3 \text{ miles}
   \]

Thus, the approximate distance from Station E to Station G is **11.3 miles**.

Would you like further clarification or details? Here are five related questions:

1. How can you find the coordinates of other points from the graph?
2. What is the formula for calculating distance between two points in 3D space?
3. Can you use other methods to estimate distance on a map besides the distance formula?
4. How would you find the distance if there were more points in between?
5. Why is the distance formula an application of the Pythagorean theorem?

**Tip:** When dealing with distance problems, always ensure you correctly identify the coordinates of the points involved.

The units of the subway map below are in miles. Suppose the routes between stations are straight. Station G, not shown on the map, is 4 miles east and 6 miles south of Station A. What is the approximate distance between Station E and Station G when traveling by subway?

Learn how to calculate the distance between Station E and Station G on a coordinate plane using the distance formula. This subway problem covers key geometry concepts and applies the Pythagorean theorem. Suitable for Grades 8-10.

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