To determine the total number of miles traveled by the boat, we will calculate the distance for each leg of the trip.
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From (7, 0) to (7, -7):
- The distance formula for points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, \((x_1, y_1) = (7, 0)\) and \((x_2, y_2) = (7, -7)\): \[ d = \sqrt{(7 - 7)^2 + (-7 - 0)^2} = \sqrt{0 + 49} = \sqrt{49} = 7 \text{ miles} \]
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From (7, -7) to (0, -7):
- Now let \((7, -7)\) and \((0, -7)\): \[ d = \sqrt{(0 - 7)^2 + (-7 - (-7))^2} = \sqrt{(-7)^2 + 0} = \sqrt{49} = 7 \text{ miles} \]
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From (0, -7) back to (7, 0):
- Now let \((0, -7)\) and \((7, 0)\): \[ d = \sqrt{(7 - 0)^2 + (0 - (-7))^2} = \sqrt{7^2 + 7^2} = \sqrt{49 + 49} = \sqrt{98} \] \[ = \sqrt{49 \times 2} = 7\sqrt{2} \text{ miles} \approx 7 \times 1.414 \approx 9.899 \text{ miles} \]
Now we add up the total distance traveled:
- Distance from (7, 0) to (7, -7): 7 miles
- Distance from (7, -7) to (0, -7): 7 miles
- Distance from (0, -7) to (7, 0): approximately 9.899 miles
Total distance traveled: \[ 7 + 7 + 9.899 \approx 23.899 \text{ miles} \]
Rounding to the nearest whole number: \[ \text{Total distance} \approx 24 \text{ miles} \]
Thus, the total number of miles traveled is 24 miles.
The answer is: d) 24 miles.
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