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

6.08
6.08

11
11

8.54

Answer 1

To find the distance between the points \((0, 6)\) and \((-3, -2)\) using the Pythagorean Theorem, we can treat the distance as the hypotenuse of a right triangle.

First, we calculate the differences in the x-coordinates and y-coordinates:

- The difference in the x-coordinates is:
\[
x_2 - x_1 = -3 - 0 = -3
\]

- The difference in the y-coordinates is:
\[
y_2 - y_1 = -2 - 6 = -8
\]

Now, we take the absolute values of these differences:
\[
|x_2 - x_1| = 3
\]
\[
|y_2 - y_1| = 8
\]

We can now use the Pythagorean Theorem to find the distance \(d\) between the points:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the values we found:
\[
d = \sqrt{(-3)^2 + (-8)^2}
\]
\[
d = \sqrt{9 + 64}
\]
\[
d = \sqrt{73}
\]

Now, we compute \(\sqrt{73}\):
\[
d \approx 8.544
\]
Rounding to the nearest hundredth gives:
\[
d \approx 8.54
\]

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