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, substituting the values into the formula:
\[ d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2} \]
Calculating each part:
- \(x_2 - x_1 = -2 - (-8) = -2 + 8 = 6\)
- \(y_2 - y_1 = -5 - (-3) = -5 + 3 = -2\)
Now substituting these results back into the distance formula:
\[ d = \sqrt{(6)^2 + (-2)^2} \]
Calculating the squares:
\[ d = \sqrt{36 + 4} = \sqrt{40} \]
Now we can simplify \(\sqrt{40}\):
\[ \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \]
Next, we can approximate \(\sqrt{10}\):
\(\sqrt{10} \approx 3.162\)
So,
\[ d \approx 2 \times 3.162 = 6.324 \]
Finally, rounding to the nearest hundredth:
\[ d \approx 6.32 \]
Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately 6.32.