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)

1 answer

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.