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

100
100

14
14

10
10

9.22

Answer 1

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

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

In this case:
- \(x_1 = -1\), \(y_1 = 6\)
- \(x_2 = 5\), \(y_2 = -2\)

Now, substitute these values into the formula:

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]

2. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = -2 - 6 = -8
\]

3. Plug these results into the distance formula:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]

4. Calculate the squares:
\[
d = \sqrt{36 + 64}
\]

5. Add the squares:
\[
d = \sqrt{100}
\]

6. Take the square root:
\[
d = 10
\]

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

The correct response is:

**10**