To find the distance between the points \((-8, -3)\) and \((-2, -5)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).
Now, substitute the values into the formula:
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Calculate the differences:
- \(x_2 - x_1 = -2 - (-8) = -2 + 8 = 6\)
- \(y_2 - y_1 = -5 - (-3) = -5 + 3 = -2\)
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Now substitute these values into the formula: \[ d = \sqrt{(6)^2 + (-2)^2} \]
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Calculate the squares: \[ d = \sqrt{36 + 4} \]
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Adding those: \[ d = \sqrt{40} \]
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Now simplify \(\sqrt{40}\): \[ d = \sqrt{4 \times 10} = 2\sqrt{10} \]
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Now, let's calculate this value. The approximate value of \(\sqrt{10}\) is about \(3.1623\), so: \[ d \approx 2 \times 3.1623 \approx 6.3246 \]
Rounding this to the nearest hundredth, we get: \[ d \approx 6.32 \]
Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(6.32\).