To find the length 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 the points \((0, 6)\) and \((-3, -2)\):
- \(x_1 = 0\), \(y_1 = 6\)
- \(x_2 = -3\), \(y_2 = -2\)
Substituting these values into the formula:
\[ d = \sqrt{((-3) - 0)^2 + ((-2) - 6)^2} \] \[ = \sqrt{(-3)^2 + (-8)^2} \] \[ = \sqrt{9 + 64} \] \[ = \sqrt{73} \]
Now, we calculate \(\sqrt{73}\).
Using a calculator:
\[ \sqrt{73} \approx 8.544 \]
Rounding to the nearest hundredth, we have:
\[ \sqrt{73} \approx 8.54 \]
Thus, the length between the points \((0, 6)\) and \((-3, -2)\) is approximately 8.54.
The correct response is:
8.54