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.
- Sledding: Given coordinates are (12, 2) and (2, 12).
- Ice Skating: Given coordinates are (-4, 2) and (2, -4).
- 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.