Question

Apply the Pythagorean Theorem to find the length between (−1, 6)
(
−
1
,

6
)
and (5, −2)
(
5
,

−
2
)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

100
100

14
14

10
10

9.22

Answer 1

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

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

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

Substituting these values into the formula:

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

Calculating the differences:

- \(x_2 - x_1 = 5 - (-1) = 5 + 1 = 6\)
- \(y_2 - y_1 = -2 - 6 = -8\)

Now substituting these differences back into the formula:

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

Calculating the squares:

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

Finally, taking the square root:

\[
d = 10
\]

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

The answer is \( \boxed{10} \).