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

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=√((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=√((8-4)^2+(12-2)^2) \\ d=√(4^2+10^2) \\ d=√(16+100) \\ d=√(116) \\ d=√(4*29) \\ d=2√(29)\text{ units} \end{gathered}`

Since, 1 unit represents 1 kilometer on the map,

Hence, the answer is

`2√(29)\text{ km}`