Question

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. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers

Answer 1

Solution:

Given the points below

$p\left(4,2\right)and\text{ }q\left(8,12\right)$

To find the distance between two points, the formula is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Where point p represents coordinates 1 and point q represents coordinates 2

Substitute the coordinates into the formula above

$\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}$

Since, 1 unit represents 1 kilometer on the map,

Hence, the answer is

$2\sqrt{29}\text{ km}$