To find the perimeter of the triangle formed by the points \( A(2, 2) \), \( B(-1, -2) \), and \( C(1, -2) \), we need to calculate the lengths of the sides of the triangle.
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Calculate side \( AB \): \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{((-1) - 2)^2 + ((-2) - 2)^2} \] \[ = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
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Calculate side \( BC \): \[ BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(1 - (-1))^2 + ((-2) - (-2))^2} \] \[ = \sqrt{(1 + 1)^2 + (0)^2} = \sqrt{(2)^2} = 2 \]
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Calculate side \( CA \): \[ CA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2 - 1)^2 + (2 - (-2))^2} \] \[ = \sqrt{(1)^2 + (4)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1231 \]
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Calculate the perimeter: \[ P = AB + BC + CA = 5 + 2 + \sqrt{17} \approx 5 + 2 + 4.1231 \approx 11.1231 \]
Rounding to the nearest tenth, the perimeter is approximately: \[ \boxed{11.1} \] units.