To find the distance between the points \((0, 6)\) and \((-3, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For our points:
- \((x_1, y_1) = (0, 6)\)
- \((x_2, y_2) = (-3, -2)\)
Substituting the coordinates into the formula:
\[ d = \sqrt{((-3) - 0)^2 + ((-2) - 6)^2} \]
Calculating the differences:
\[ = \sqrt{(-3)^2 + (-8)^2} \]
Calculating the squares:
\[ = \sqrt{9 + 64} \] \[ = \sqrt{73} \]
Now, we can calculate \(\sqrt{73}\):
\[ \sqrt{73} \approx 8.544 \]
Rounding to the nearest hundredth gives:
\[ \approx 8.54 \]
Thus, the length between the points \((0, 6)\) and \((-3, -2)\) is 8.54.