Question

why is the distance formula important for gps systems? a. to play music b. to determine the weather c. to calculate the shortest routes d. to read books a drone flies from (1, 1) to (4, 5). using the distance formula, calculate its flight distance. a. $sqrt{16}$ units b. 6 units c. $sqrt{25}$ units d. 3 units

Explanation:

Step1: Recall purpose of GPS

GPS is for navigation and finding routes.

Step2: Analyze options

Options a, b and d are unrelated to distance - formula use in GPS. The distance formula helps calculate shortest routes in GPS systems.

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify points

Here, $(x_1,y_1)=(1,1)$ and $(x_2,y_2)=(4,5)$.

Step3: Substitute values

$d=\sqrt{(4 - 1)^2+(5 - 1)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}$.

Answer:

c. To calculate the shortest routes