To solve Part C and D, let's assume we have the relevant coordinates for each school and then analyze each step.
Part C: Find the Shortest Distance
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Identify the Coordinates: Assume:
- Math Middle School (M) is at point (x1, y1).
- Hypotenuse High School (H) is at point (x2, y2). Let's use hypothetical coordinates for illustration:
- M: (2, 3)
- H: (8, 7)
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Calculate the Distance Using the Distance Formula: The distance \( d \) between two points \((x1, y1)\) and \((x2, y2)\) is calculated using the formula:
\[ d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]
Plugging in our hypothetical values:
\[ d = \sqrt{(8 - 2)^2 + (7 - 3)^2} \] \[ d = \sqrt{(6)^2 + (4)^2} \] \[ d = \sqrt{36 + 16} \] \[ d = \sqrt{52} \] \[ d \approx 7.21 \text{ miles} \]
Therefore, the distance from Math Middle School to Hypotenuse High School is approximately 7.21 miles.
Part D: Analyze Travel Distances
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Distance Traveled by Deon:
- Deon goes from Hypotenuse High (H) to Euclid Elementary (E) and then to Math Middle (M).
- Assume Euclid Elementary is at (x3, y3). For example, let’s say E: (5, 5).
- First, calculate the distance from H to E:
\[ d_{HE} = \sqrt{(5 - 8)^2 + (5 - 7)^2} \] \[ = \sqrt{(-3)^2 + (-2)^2} \] \[ = \sqrt{9 + 4} \] \[ = \sqrt{13} \approx 3.61 \text{ miles} \]
- Then calculate the distance from E to M:
\[ d_{EM} = \sqrt{(2 - 5)^2 + (3 - 5)^2} \] \[ = \sqrt{(-3)^2 + (-2)^2} \] \[ = \sqrt{9 + 4} \] \[ = \sqrt{13} \approx 3.61 \text{ miles} \]
- Total distance traveled by Deon:
\[ d_{Deon} = d_{HE} + d_{EM} \approx 3.61 + 3.61 \approx 7.22 \text{ miles} \]
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Distance Traveled by Kaya:
- Kaya travels directly from H to M, which we already calculated as approximately 7.21 miles.
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Comparison:
- Deon's total distance is approximately: 7.22 miles.
- Kaya's distance is approximately: 7.21 miles.
Conclusion:
Kaya went the shortest distance, as her total distance of approximately 7.21 miles is less than Deon's total distance of approximately 7.22 miles. Therefore, Kaya took the more direct route straight from Hypotenuse High to Math Middle, while Deon took a longer indirect path.