Question

Please help with the problem shown in the screen shot, i dont know how to solve.

Answer 1

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.

`(x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,0)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-2-0)^2 + (1-0)^2)\\\\d = √((-2)^2 + (1)^2)\\\\d = √(4 + 1)\\\\d = √(5)\\\\d \approx 2.236068\\\\`

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

`(x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (5,-5)\\\\d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((0-5)^2 + (0-(-5))^2)\\\\d = √((0-5)^2 + (0+5)^2)\\\\d = √((-5)^2 + (5)^2)\\\\d = √(25 + 25)\\\\d = √(50)\\\\d = √(25*2)\\\\d = √(25)*√(2)\\\\d = 5√(2)\\\\d \approx 7.071068\\\\`

The total exact distance traveled, when moving along the green subway lines, is
`EA+AG = √(5)+5√(2)`

Use a calculator to find that
`√(5)+5√(2) \approx 9.3071 \approx 9.3`

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