Question

pythagorean theorem study guide
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
ann
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 $y_2 - y_1=-10 - 3=-13$.

Step3: Calculate the square - sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=7^2+(-13)^2=49 + 169=218$.

Step4: Find the distance in units

$d=\sqrt{218}\approx14.76$ units.

Step5: Convert units to feet

Since each unit represents 2 feet, the distance in feet is $2\times\sqrt{218}\approx2\times14.76 = 29.52\approx30$ feet.

Answer:

30