Question

Apply the Pythagorean Theorem to find the length between (0, 6)
and (−3, −2)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

6.08
6.08

73
73

11
11

8.54

Answer 1

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**.