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

8.54
8.54

11

Answer 1

To find the distance between the points \((0, 6)\) and \((-3, -2)\) using the Pythagorean Theorem, we can apply the distance formula:

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

Here, let \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).

Now substitute the coordinates into the formula:

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

This simplifies to:

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

Calculating the squares:

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

Adding these together:

\[
d = \sqrt{73}
\]

Now, to get the approximate distance, we can use a calculator:

\[
d \approx 8.54
\]

Therefore, the length between the points (0, 6) and (-3, -2) is approximately **8.54**.

So the correct response is:

**8.54**