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 9.22 100 100 10 10 14

Answer 1

To find the length between the points \((-1, 6)\) and \((5, -2)\), we can apply the Pythagorean Theorem, which can be expressed using 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 values into the formula, we have:

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

Calculating the differences:

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

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

Now calculate the squares:

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

\[
= \sqrt{100}
\]

Finally, take the square root:

\[
d = 10
\]

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

Thus, the final answer is:

**10**