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 9.22 9.22 14 14 100

Answer 1

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

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

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

Now we can calculate the values:

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

Now plug these into the distance formula:

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

Calculating the squares:

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

Therefore,

\[
d = 10
\]

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

The final answer is **10**.