Question

select the correct answer
on a map where each unit represents one kilometer, two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other, how far does the boat travel?
a. 14 kilometers
b. 2\sqrt{29} kilometers
c. 6 kilometers
d. 2\sqrt{5} kilometers

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(4,2)$ and $(x_2,y_2)=(8,12)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=8 - 4 = 4$ and $y_2 - y_1=12 - 2 = 10$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{4^2 + 10^2}=\sqrt{16+100}=\sqrt{116}$.

Step4: Simplify the square - root

Simplify $\sqrt{116}=\sqrt{4\times29}=2\sqrt{29}$.

Answer:

B. $2\sqrt{29}$ kilometers