Question

i can apply the pythagorean theorem to find distance on a coordinate plane. the point on the graph represents anns location. she is using a metal detector on the beach to see what she can find. each unit on the graph represents 2 feet. #24. a pile of bottle caps is located at (4, - 10). find the length of the most direct path between ann and the pile of bottle caps. the length of the most directed path between ann and the pile of bottle caps is feet.

Explanation:

Step1: Determine Ann's coordinates

Ann is at (-3, 3).

Step2: Use distance formula derived from Pythagorean theorem

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, $(x_1,y_1)=(-3,3)$ and $(x_2,y_2)=(4,-10)$. First find the differences: $x_2 - x_1=4-(-3)=7$ and $y_2 - y_1=- 10 - 3=-13$. Then square them: $(x_2 - x_1)^2 = 7^2 = 49$ and $(y_2 - y_1)^2=(-13)^2 = 169$. Add them: $49 + 169=218$. So the distance in units is $d=\sqrt{218}$.

Step3: Convert units to feet

Since each unit represents 2 feet, the distance in feet is $2\sqrt{218}\approx2\times14.765 = 29.53\approx30$ feet.

Answer:

30