Bot GPT 4-o mini To calculate the total distance traveled between the locations, we will calculate the distances between the points: sledding (2, 12), ice skating (2, -4), and skiing (-8, -4).
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Distance from sledding to ice skating:
- Points: (2, 12) to (2, -4)
- The distance is calculated using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, \( x_1 = 2, y_1 = 12 \) and \( x_2 = 2, y_2 = -4 \): \[ d = \sqrt{(2 - 2)^2 + (-4 - 12)^2} = \sqrt{0 + (-16)^2} = \sqrt{256} = 16 \]
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Distance from ice skating to skiing:
- Points: (2, -4) to (-8, -4)
- Similarly, we use the distance formula: \[ d = \sqrt{(-8 - 2)^2 + (-4 - (-4))^2} \]
- Here, \( x_1 = 2, y_1 = -4 \) and \( x_2 = -8, y_2 = -4 \): \[ d = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10 \]
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Total distance traveled:
- To find the total distance, we add the distances from step 1 and step 2: \[ \text{Total Distance} = 16 + 10 = 26 \]
Therefore, the total distance traveled between these locations is 26 units.
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