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?

the drone flies kilometers

Explanation:

Step1: Find the coordinates

The coordinates of home are \((3,1)\) and of park are \((-2,-2)\).

Step2: Use the 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 \(x_1 = 3,y_1 = 1,x_2=-2,y_2 = -2\).

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Since 1 unit \( = 2\) km, multiply the distance in units by 2.
The distance in units is \(\sqrt{34}\approx5.83\) units.
The distance in km is \(2\times\sqrt{(3+2)^2+(1 + 2)^2}=2\times\sqrt{25 + 9}=2\times\sqrt{34}\approx 10\) (by counting units: horizontal change \(3-(-2)=5\) units, vertical change \(1-(-2)=3\) units. Using Pythagorean theorem \(d=\sqrt{5^2+3^2}=\sqrt{25 + 9}=\sqrt{34}\approx5\) units (approximate counting), then \(2\times5 = 10\))

Answer:

\(10\)