Apply the Pythagorean Theorem to find the length between (0, 6)

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 the points \((0, 6)\) and \((-3, -2)\):

• \(x_1 = 0\), \(y_1 = 6\)
• \(x_2 = -3\), \(y_2 = -2\)

Now we plug in the values:

\[ d = \sqrt{((-3) - 0)^2 + ((-2) - 6)^2} \] \[ d = \sqrt{(-3)^2 + (-8)^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]

Now, we'll calculate \(\sqrt{73}\).

Using a calculator:

\[ \sqrt{73} \approx 8.54 \]

So, rounding to the nearest hundredth, the distance between the points \((0, 6)\) and \((-3, -2)\) is approximately 8.54.

The correct response is:

8.54