Answer: 9.3
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Step-by-step explanation
Station E is marked on the map at location (-2,1)
Station G is not marked on the map, but it's at location (5,-5) since we go 5 miles east and 5 miles south of station A.
Station A is at the origin (0,0).
To go from E to G, we need to go through station A. We must follow the green lines.
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The first thing to do is find the distance from E to A.
I'll use the distance formula.

Then we need to find the distance from A to G.

The total exact distance traveled, when moving along the green subway lines, is

Use a calculator to find that

Therefore, we must travel approximately 9.3 miles when going from E to A to G along the green subway lines.