To find which of the given points has a distance of 10 from the point \((-1, 2)\), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) is the point \((-1, 2)\) and \((x_2, y_2)\) is the point we are checking.
Let's check each point:
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Point (10, 2): \[ d = \sqrt{(10 - (-1))^2 + (2 - 2)^2} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11 \] (Distance is 11)
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Point (-1, -12): \[ d = \sqrt{(-1 - (-1))^2 + (-12 - 2)^2} = \sqrt{(0)^2 + (-14)^2} = \sqrt{196} = 14 \] (Distance is 14)
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Point (-11, 2): \[ d = \sqrt{(-11 - (-1))^2 + (2 - 2)^2} = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10 \] (Distance is 10)
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Point (-1, 10): \[ d = \sqrt{(-1 - (-1))^2 + (10 - 2)^2} = \sqrt{(0)^2 + (8)^2} = \sqrt{64} = 8 \] (Distance is 8)
From these calculations, we find that the point (-11, 2) has a distance of 10 from the point \((-1, 2)\).