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

10
10

100
100

14
14

9.22

Answer 1

To find the length between the points \((-1, 6)\) and \( (5, -2)\), we can use the Pythagorean Theorem, which is applicable to the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

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

Substituting the values:

\[
x_1 = -1, \quad y_1 = 6, \quad x_2 = 5, \quad y_2 = -2
\]

Now, plug these values into the distance formula:

\[
d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(5 + 1)^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

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

So, the correct response is:

**10**