To find the perimeter of the parallelogram with vertices at (2, 1), (2, 3), (4, 4), and (4, 2), we first need to determine the lengths of the sides.
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Identify the Lengths of the Sides:
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Side between (2, 1) and (2, 3): \[ \text{Length} = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2 \]
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Side between (2, 3) and (4, 4): \[ \text{Length} = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236 \]
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Side between (4, 4) and (4, 2): \[ \text{Length} = \sqrt{(4 - 4)^2 + (2 - 4)^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2 \]
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Side between (4, 2) and (2, 1): \[ \text{Length} = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236 \]
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Calculate the Perimeter: The perimeter \( P \) of the parallelogram is given by the sum of the lengths of all sides: \[ P = 2 + 2.236 + 2 + 2.236 = 8.472 \]
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Round to the Nearest Tenth: \[ P \approx 8.5 \]
Thus, the perimeter of the parallelogram is approximately 8.5 units.