A lake fishing map is laid out on a coordinate plane with each unit equal to 1 mile. The boat is launched from the point (7, 0) and goes to point (7, −7) to fish. From there, the boat travels to (0, −7) to fish and then goes back to the launch point.
Determine the total number of miles traveled. Round to the nearest whole number.
a) 10 miles
b) 12 miles
c) 14 miles
d) 24 miles
To find the total distance traveled, we need to calculate the distance between each pair of points.
First, let's calculate the distance from (7, 0) to (7, -7):
- The x-coordinate remains the same, so the change in x is 0.
- The y-coordinate decreases by 7 units, so the change in y is 7.
Using the distance formula, the distance is sqrt((0-0)^2 + (7-0)^2) = sqrt(0 + 49) = sqrt(49) = 7 miles.
Next, let's calculate the distance from (7, -7) to (0, -7):
- The y-coordinate remains the same, so the change in y is 0.
- The x-coordinate decreases by 7 units, so the change in x is 7.
Using the distance formula, the distance is sqrt((0-7)^2 + (0-(-7))^2) = sqrt((-7)^2 + 7^2) = sqrt(49 + 49) = sqrt(98) ≈ 9.899 miles (rounded to the nearest whole number).
Finally, let's calculate the distance from (0, -7) back to the launch point at (7, 0):
- The y-coordinate increases by 7 units, so the change in y is -(-7) = 7.
- The x-coordinate increases by 7 units, so the change in x is 7.
Using the distance formula, the distance is sqrt((7-0)^2 + (7-(-7))^2) = sqrt(7^2 + 14^2) = sqrt(49 + 196) = sqrt(245) ≈ 15.652 miles (rounded to the nearest whole number).
Therefore, the total distance traveled is 7 + 9.899 + 15.652 ≈ 32.55 miles (rounded to the nearest whole number) ,which is approximately 33 miles. None of the given answer options is correct.