To find the distance between the points \((-8, -3)\) and \((-2, -5)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).
Now, plug in the coordinates into the formula:
\[ d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2} \]
Calculating each part:
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Calculate \(x_2 - x_1\): \[ -2 - (-8) = -2 + 8 = 6 \]
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Calculate \(y_2 - y_1\): \[ -5 - (-3) = -5 + 3 = -2 \]
Now, substitute these values back into the formula:
\[ d = \sqrt{(6)^2 + (-2)^2} \]
Calculating the squares:
\[ d = \sqrt{36 + 4} = \sqrt{40} \]
Now, simplify \(\sqrt{40}\):
\[ \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \]
To evaluate \(2\sqrt{10}\), we can find \(\sqrt{10} \approx 3.1623\):
\[ d \approx 2 \times 3.1623 \approx 6.3246 \]
Rounding to the nearest hundredth:
\[ d \approx 6.32 \]
Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(6.32\).