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

73
73

8.54
8.54

11
11

6.08

Answer 1

To find the distance between the points \( (0, 6) \) and \( (-3, -2) \) using the Pythagorean Theorem, we can utilize the distance formula, which is derived from the theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Now, substituting the coordinates of the points \( (0, 6) \) and \( (-3, -2) \):

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

Substituting these values into the distance formula:

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

Calculating the differences:

\[
d = \sqrt{(-3)^2 + (-8)^2}
\]

Calculating the squares:

\[
d = \sqrt{9 + 64}
\]

Adding the squares:

\[
d = \sqrt{73}
\]

Now, to find the numerical value of \( \sqrt{73} \):

\[
d \approx 8.54
\]

Thus, the distance between the points \( (0, 6) \) and \( (-3, -2) \) is approximately \( 8.54 \). Therefore, rounding it to the nearest hundredth, the answer is:

**8.54**