Question

a scientist is studying the migration pattern of a particular species of sea turtle. she was able to track one turtles location from its starting map coordinates (6, 25) to the map coordinates (44, 58) in a day. if each unit in the map coordinates represents 1 mile, how far away from the starting point did the turtle end up? round your answer to the nearest tenth.

Explanation:

Step1: Identify the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(6,25)$ and $(x_2,y_2)=(44,58)$.

Step2: Calculate the differences

$x_2 - x_1=44 - 6 = 38$ and $y_2 - y_1=58 - 25 = 33$.

Step3: Square the differences

$(x_2 - x_1)^2=38^2 = 1444$ and $(y_2 - y_1)^2=33^2 = 1089$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=1444 + 1089=2533$.

Step5: Calculate the square - root

$d=\sqrt{2533}\approx50.3$.

Answer:

$50.3$ miles