To determine who went the shortest distance between Deon and Kaya, we need to calculate the distances for both.
Deon's Route (Hypotenuse High to Euclid Elementary to Math Middle):
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Distance from Hypotenuse High (−4, −3) to Euclid Elementary (−4, 1):
- The distance is calculated using the formula for the distance between two points: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, \( (x_1, y_1) = (-4, -3) \) and \( (x_2, y_2) = (-4, 1) \): \[ d = \sqrt{(-4 - (-4))^2 + (1 - (-3))^2} = \sqrt{0^2 + (1 + 3)^2} = \sqrt{0 + 4^2} = \sqrt{16} = 4 \text{ miles} \]
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Distance from Euclid Elementary (−4, 1) to Math Middle (1, 1):
- Again, using the distance formula with \( (x_1, y_1) = (-4, 1) \) and \( (x_2, y_2) = (1, 1) \): \[ d = \sqrt{(1 - (-4))^2 + (1 - 1)^2} = \sqrt{(1 + 4)^2 + 0^2} = \sqrt{5^2 + 0} = \sqrt{25} = 5 \text{ miles} \]
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Total Distance for Deon: \[ \text{Total Distance} = 4 \text{ miles} + 5 \text{ miles} = 9 \text{ miles} \]
Kaya's Route (Hypotenuse High to Math Middle directly):
- Distance from Hypotenuse High (−4, −3) to Math Middle (1, 1):
- Using the distance formula with \( (x_1, y_1) = (-4, -3) \) and \( (x_2, y_2) = (1, 1) \): \[ d = \sqrt{(1 - (-4))^2 + (1 - (-3))^2} = \sqrt{(1 + 4)^2 + (1 + 3)^2} = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41} \approx 6.4 \text{ miles} \]
Final Comparison:
- Deon's total distance = 9 miles
- Kaya's distance = \(\sqrt{41} \approx 6.4\) miles
Since \(6.4\) miles (Kaya) is shorter than \(9\) miles (Deon), Kaya traveled the shortest distance.
Answer: Kaya went the shortest distance, traveling approximately 6.4 miles, compared to Deon's 9 miles.