Question

sara is considering charging her electric car. if she goes to the charging station on the following map, she will have to drive farther than if she drove straight to her destination.
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: Identify Coordinates

First, we find the coordinates of each point. The car is at \((-3, 2)\), the charging station is at \((5, -3)\), and the destination is at \((7, 3)\).

Step2: Calculate Distance from Car to Destination (Straight Path)

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), for car \((-3, 2)\) and destination \((7, 3)\):

$$
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$$

Step3: Calculate Distance from Car to Charging Station

For car \((-3, 2)\) and charging station \((5, -3)\):

$$
LATEXBLOCK1
$$

Step4: Calculate Distance from Charging Station to Destination

For charging station \((5, -3)\) and destination \((7, 3)\):

$$
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$$

Step5: Calculate Total Distance via Charging Station

Add the two distances: \(d_{total - cs} = 9.43 + 6.32 = 15.75\)

Step6: Find the Difference

Subtract the straight path distance from the total distance via charging station: \(15.75 - 10.05 \approx 5.7\), which rounds to 6.

Answer:

6