Question

Shahriyar is at a winter park with his family they go sledding first then ice skating then skiing what is the total distance traveled between these location ice skating (2, -4) or skiing (-4, -8) sledding (2, 12) to miles

Answer 1

To calculate the total distance traveled between the three locations (sledding, ice skating, and skiing), we need to find the distances between each pair of points using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given the coordinates:
- Sledding: (2, 12)
- Ice Skating: (2, -4)
- Skiing: (-4, -8)

### Step 1: Calculate the distance from Sledding to Ice Skating

Let \( (x_1, y_1) = (2, 12) \) and \( (x_2, y_2) = (2, -4) \).

\[
d_{\text{sledding to ice skating}} = \sqrt{(2 - 2)^2 + (-4 - 12)^2}
\]
\[
= \sqrt{0 + (-16)^2}
\]
\[
= \sqrt{256} = 16
\]

### Step 2: Calculate the distance from Ice Skating to Skiing

Let \( (x_1, y_1) = (2, -4) \) and \( (x_2, y_2) = (-4, -8) \).

\[
d_{\text{ice skating to skiing}} = \sqrt{(-4 - 2)^2 + (-8 + 4)^2}
\]
\[
= \sqrt{(-6)^2 + (-4)^2}
\]
\[
= \sqrt{36 + 16}
\]
\[
= \sqrt{52} = 2\sqrt{13} \approx 7.21
\]

### Step 3: Calculate the total distance traveled

Now, sum the two distances:

\[
\text{Total Distance} = 16 + 2\sqrt{13}
\]

### Approximate Value

\[
2\sqrt{13} \approx 7.21
\]
So,

\[
\text{Total Distance} \approx 16 + 7.21 \approx 23.21
\]

### Conclusion

The total distance traveled is approximately **23.21 miles**.