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

14
14

100
100

10
10

9.22

Answer 1

To find the distance between the two points \((-1, 6)\) and \( (5, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem:

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

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

Substituting the values into the formula:

1. Calculate \(x_2 - x_1\):

\[
5 - (-1) = 5 + 1 = 6
\]

2. Calculate \(y_2 - y_1\):

\[
-2 - 6 = -8
\]

3. Now plug these values into the distance formula:

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

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

The correct response is **10**.