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

9.22
9.22

10
10

100

Answer 1

To find the length between the points \((-1, 6)\) and \((5, -2)\), we will use the distance formula, which is derived from the Pythagorean theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In our case, the points are \((-1, 6)\) and \((5, -2)\). So, we can identify:

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

Now substitute the values into the distance formula:

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

Calculating the differences:

- \(5 - (-1) = 5 + 1 = 6\)
- \(-2 - 6 = -8\)

Now substitute these results back into the formula:

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

Calculating the squares:

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

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

The closest response is:
**10**.