Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. krista pilots a drone from her house to the park. the relative locations are shown in the coordinate plane. what is the distance the drone flies? 1 unit = 2 km the drone flies kilometers.

Explanation:

Step1: Identify coordinates

Let the home's coordinates be $(3,1)$ and the park's coordinates be $(- 2,-2)$.

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1=1,x_2=-2,y_2 = - 2$. So $d=\sqrt{(-2 - 3)^2+(-2 - 1)^2}=\sqrt{(-5)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34}$.

Step3: Convert to actual distance

Since 1 unit = 2 km, the actual distance $D = 2\sqrt{34}\approx2\times5.831 = 11.662\approx11.66$ km.

Answer:

$2\sqrt{34}$