Question

1 week streak!
coordinate values on the map are in kilometers.
how much shorter is the path straight to the destination than past the charging station?
round your final answer only to the nearest kilometer.
\boxed{} km

Explanation:

Step1: Find coordinates

Let's assume the car's coordinate is \((-2,2)\), the charging station's coordinate is \((3,-3)\), and the destination's coordinate is \((6,3)\).

Step2: Calculate distance via charging station

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Distance from car to charging station: \(d_1=\sqrt{(3 - (-2))^2+(-3 - 2)^2}=\sqrt{25 + 25}=\sqrt{50}\approx7.07\)
Distance from charging station to destination: \(d_2=\sqrt{(6 - 3)^2+(3 - (-3))^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.71\)
Total distance via charging station: \(D_1=d_1 + d_2\approx7.07+6.71 = 13.78\)

Step3: Calculate straight - line distance

Distance from car to destination: \(D_2=\sqrt{(6 - (-2))^2+(3 - 2)^2}=\sqrt{64 + 1}=\sqrt{65}\approx8.06\)

Step4: Find the difference

\(\Delta D=D_1 - D_2\approx13.78 - 8.06 = 5.72\approx6\)

Answer:

\(6\)