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
#23 a piece of jewelry is located at (7, 6). find the length of the most direct path between ann and the jewelry.
the length of the most directed path between ann and the jewelry is feet

Explanation:

Step1: Determine Ann's coordinates

Ann is at (-2, 3).

Step2: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Let $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(7,6)$. Then $d=\sqrt{(7 - (-2))^2+(6 - 3)^2}=\sqrt{(7 + 2)^2+3^2}=\sqrt{9^2+3^2}=\sqrt{81 + 9}=\sqrt{90}=3\sqrt{10}$.

Step3: Adjust for scale

Since each unit represents 2 feet, the actual distance is $2\times3\sqrt{10}=6\sqrt{10}\approx 6\times3.162 = 18.972\approx19$ feet.

Answer:

19