To calculate the total distance traveled by Shahririyar, we will first find the distances between each pair of locations:
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Distance from sledding at (2, 12) to ice skating at (2, -4): The two points have the same x-coordinate (2). Therefore, the distance can be calculated using the absolute difference in the y-coordinates: \[ \text{Distance} = |12 - (-4)| = |12 + 4| = |16| = 16 \]
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Distance from ice skating at (2, -4) to skiing at (-8, -4): The two points have the same y-coordinate (-4). Therefore, the distance can be calculated using the absolute difference in the x-coordinates: \[ \text{Distance} = |-8 - 2| = |-10| = 10 \]
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Total distance traveled: Now, we add the distances calculated: \[ \text{Total Distance} = 16 + 10 = 26 \]
Therefore, the total distance traveled between these locations is \( \boxed{26} \).