To calculate the total distance traveled by Shahriyar and his family during their winter activities, we can find the distances between the locations in the order they visited: sledding, ice skating, and then skiing.
- Distance from Sledding (2, 12) to Ice Skating (2, -4):
Using the distance formula, \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here:
- \( (x_1, y_1) = (2, 12) \)
- \( (x_2, y_2) = (2, -4) \)
Calculating the distance: \[ d_1 = \sqrt{(2 - 2)^2 + (-4 - 12)^2} = \sqrt{0 + (-16)^2} = \sqrt{256} = 16 \]
- Distance from Ice Skating (2, -4) to Skiing (-8, -4):
Using the distance formula again:
- \( (x_1, y_1) = (2, -4) \)
- \( (x_2, y_2) = (-8, -4) \)
Calculating the distance: \[ d_2 = \sqrt{(-8 - 2)^2 + (-4 - (-4))^2} = \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10 \]
- Total Distance Traveled:
By adding both distances: \[ \text{Total Distance} = d_1 + d_2 = 16 + 10 = 26 \]
Thus, the total distance traveled between these locations is 26 units.