Question

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

Answer 1

To determine the total number of miles traveled by the boat, we will calculate the distance for each leg of the trip.

1. **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 \((x_2, y_2) = (7, -7)\):
\[
d = \sqrt{(7 - 7)^2 + (-7 - 0)^2} = \sqrt{0 + 49} = \sqrt{49} = 7 \text{ miles}
\]

2. **From (7, -7) to (0, -7)**:
- Now let \((7, -7)\) and \((0, -7)\):
\[
d = \sqrt{(0 - 7)^2 + (-7 - (-7))^2} = \sqrt{(-7)^2 + 0} = \sqrt{49} = 7 \text{ miles}
\]

3. **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**.