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

10
10

100
100

14
14
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Answer 1

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

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

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

Now, we calculate:

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

Now we plug these values into the distance formula:

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

Calculating the squares:

\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

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

The correct response is:

**10**