To find the distance between the two points \((-7, -4)\) and \((3, -6)\), we can use the distance formula:
\[ d = \sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2} \]
Here, \( (x_1, y_1) = (-7, -4) \) and \( (x_2, y_2) = (3, -6) \).
Plugging in the coordinates into the formula:
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Calculate \(x_2 - x_1\): \[ x_2 - x_1 = 3 - (-7) = 3 + 7 = 10 \]
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Calculate \(y_2 - y_1\): \[ y_2 - y_1 = -6 - (-4) = -6 + 4 = -2 \]
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Substitute into the distance formula: \[ d = \sqrt{{(10)}^2 + {(-2)}^2} \] \[ d = \sqrt{100 + 4} = \sqrt{104} \]
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Calculate \(\sqrt{104}\): \[ \sqrt{104} \approx 10.198 \quad (\text{using a calculator}) \]
Now rounding to the nearest tenth: \[ 10.198 \approx 10.2 \]
Therefore, the distance between the two points is approximately \(\boxed{10.2}\).
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