Question

during the archaeological dig of a shipwreck near st. augustine, a bronze bell and a pewter spoon were found. what is the distance between the artifacts if each grid represents 1 foot? round to the nearest tenth, if necessary. a) 221 feet b) 22.0 feet c) 14.9 feet d) 4.6 feet

Explanation:

Step1: Identify 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, $(x_1,y_1)=(2,14)$ and $(x_2,y_2)=(12,3)$.

Step2: Calculate differences

$x_2 - x_1=12 - 2 = 10$ and $y_2 - y_1=3 - 14=- 11$.

Step3: Square the differences

$(x_2 - x_1)^2=10^2 = 100$ and $(y_2 - y_1)^2=(-11)^2 = 121$.

Step4: Sum squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=100 + 121=221$.

Step5: Take square - root

$d=\sqrt{221}\approx14.9$ (rounded to the nearest tenth).

Answer:

C. 14.9 feet