To find the distance between the two points \((9, 2)\) and \((3, 6)\), we can use the distance formula given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1) = (9, 2)\) and \((x_2, y_2) = (3, 6)\).
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First, calculate the differences in the coordinates:
- \(x_2 - x_1 = 3 - 9 = -6\)
- \(y_2 - y_1 = 6 - 2 = 4\)
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Substitute these differences back into the formula: \[ d = \sqrt{(-6)^2 + (4)^2} \]
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Calculate the squares:
- \((-6)^2 = 36\)
- \(4^2 = 16\)
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Add the squares: \[ d = \sqrt{36 + 16} = \sqrt{52} \]
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Simplify \(\sqrt{52}\): \[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
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Calculate the approximate value of \( \sqrt{13} \): \[ \sqrt{13} \approx 3.60555 \quad (\text{using a calculator}) \] Therefore: \[ d \approx 2 \times 3.60555 = 7.2111 \]
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Finally, round this value to the nearest tenth: \[ d \approx 7.2 \]
Thus, the distance between the two points, rounded to the nearest tenth of a unit, is \(\boxed{7.2}\) units.
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