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.

Explanation:

Step1: Find distance from car to destination

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let car's coordinates be $(-2,2)$ and destination's be $(6,3)$. Then $d_1=\sqrt{(6 - (-2))^2+(3 - 2)^2}=\sqrt{8^2 + 1^2}=\sqrt{64+1}=\sqrt{65}\approx 8.06$ km.

Step2: Find distance from car to charging - station and then to destination

Car to charging - station: Let charging - station's coordinates be $(3,-3)$. $d_{car - cs}=\sqrt{(3 - (-2))^2+(-3 - 2)^2}=\sqrt{5^2+(-5)^2}=\sqrt{25 + 25}=\sqrt{50}\approx 7.07$ km. Charging - station to destination: $d_{cs - dest}=\sqrt{(6 - 3)^2+(3-(-3))^2}=\sqrt{3^2+6^2}=\sqrt{9 + 36}=\sqrt{45}\approx 6.71$ km. Total distance $d_2=d_{car - cs}+d_{cs - dest}\approx7.07 + 6.71=13.78$ km.

Step3: Find difference in distances

$d = d_2 - d_1\approx13.78-8.06 = 5.72\approx6$ km.

Answer:

6