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 the importance of distance formula for GPS

The distance formula helps in finding the shortest - path between two points. GPS systems use it to calculate the shortest routes for navigation.

Step2: Recall the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $(1,1)$ and $(4,5)$, we have $x_1 = 1,y_1 = 1,x_2 = 4,y_2 = 5$.

Step3: Substitute values into the formula

$d=\sqrt{(4 - 1)^2+(5 - 1)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$. But we check the options in terms of the non - simplified square - root form first.

Answer:

1. c. To calculate the shortest routes
2. c. $\sqrt{25}$ units