Answer:
Sally is 10 miles
The coordinate ofthe deli is (1, -1)
Step-by-step explanation:
✍️Coordinate of Sally = (-3, 2)
Coordinate of Ocean Front = (5, -4)
The distance of Sally to Ocean Front Housing Complex = the distance between point (-3, 2) and (5, -4).
Use the distance formula,
, to calculate the distance between (-3, 2) and (5, -4):
![d = \sqrt{(5 -(-3))^2 + (-4 - 2)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%285%20-%28-3%29%29%5E2%20%2B%20%28-4%20-%202%29%5E2%7D%20)
![d = \sqrt{(8)^2 + (-6)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%288%29%5E2%20%2B%20%28-6%29%5E2%7D%20)
![d = \sqrt{64 + 36}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B64%20%2B%2036%7D%20)
![d = \sqrt{100} = 10](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B100%7D%20%3D%2010%20)
✅The distance of Sally is 10 miles
✍️the coordinate of Deli would be half the distance between Sally and Ocean Front.
Therefore, use the midpoint formula to calculate the coordinate of the midpoint between Sally (-3, 2) and Ocean Front (5, -4).
Midpoint of (-3, 2) and (5, -4).
![M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29%20)
Plug in the values
![M(\frac{-3 + 5}{2}, \frac{2 +(-4)}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7B-3%20%2B%205%7D%7B2%7D%2C%20%5Cfrac%7B2%20%2B%28-4%29%7D%7B2%7D%29%20)
![M(\frac{2}{2}, \frac{-2}{2})](https://tex.z-dn.net/?f=%20M%28%5Cfrac%7B2%7D%7B2%7D%2C%20%5Cfrac%7B-2%7D%7B2%7D%29%20)
![M(1, -1)](https://tex.z-dn.net/?f=%20M%281%2C%20-1%29%20)
✅The coordinate ofthe deli is (1, -1)