Question

Apply the Pythagorean Theorem to find the length between (−1, 6)
and (5, −2)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

9.22
9.22

10
10

100
100

14

Answer 1

To find the distance between the points \((-1, 6)\) and \( (5, -2)\), 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:

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

Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).

Now plug in the values:

\[
d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2}
\]

Calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[
x_2 - x_1 = 5 + 1 = 6
\]
\[
y_2 - y_1 = -2 - 6 = -8
\]

Now substitute these into the distance formula:

\[
d = \sqrt{(6)^2 + (-8)^2}
\]

Calculate the squares:

\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]

Now find the square root:

\[
d = 10
\]

Thus, the length between the points \((-1, 6)\) and \( (5, -2)\) is \(10\).

Rounded to the nearest hundredth, the answer remains:

**10**