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

10
10

100
100

9.22
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:

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

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

Substituting the coordinates into the formula:

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

Calculating the differences:

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

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

Therefore, the answer is:

10