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A city has weather stations at \(A(1, 1)\), \(B(5, 1)\), and \(C(3, 5)\).
The temperatures recorded are: \(A: 20^\circ\text{C}\), \(B: 22^\circ\text{C}\), \(C: 18^\circ\text{C}\).
Estimate the temperature at point \(P(2, 2)\) using nearest neighbor interpolation.
  1. Calculate \(PA^2\), \(PB^2\), and \(PC^2\).
  2. Which region contains \(P\)?
  3. What is the estimated temperature?

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