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 (-4, 2) or (2, -4) skiing (-8, -4) (-4, -8) sledding (12, 2) (2, 12)

Answer 1

To find the total distance traveled between the locations of sledding, ice skating, and skiing, we first need to identify the coordinates associated with each activity from the given options.

1. **Sledding**: Given coordinates are (12, 2) and (2, 12).
2. **Ice Skating**: Given coordinates are (-4, 2) and (2, -4).
3. **Skiing**: Given coordinates are (-8, -4) and (-4, -8).

Choosing one point from each activity, we can calculate the total distance traveled. Let's select:
- Sledding: (12, 2)
- Ice Skating: (-4, 2)
- Skiing: (-8, -4)

Now, we will calculate the distances between these points.

### Distance from Sledding to Ice Skating
Using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\):

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

### Distance from Ice Skating to Skiing
\[
d_{ice\ skating \to skiing} = \sqrt{((-8) - (-4))^2 + ((-4) - 2)^2}
\]
\[
= \sqrt{(-4)^2 + (-6)^2}
\]
\[
= \sqrt{16 + 36}
\]
\[
= \sqrt{52} \approx 7.21
\]

### Total Distance Traveled
Now, we add the two distances together:
\[
\text{Total Distance} = d_{sledding \to ice\ skating} + d_{ice\ skating \to skiing}
\]
\[
= 16 + 7.21 \approx 23.21
\]

Therefore, the total distance traveled is approximately **23.21 units**.