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 10 10 9.22 9.22 100

Answer 1

To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we can use the distance formula, which is derived from it. 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 this case:
- \((x_1, y_1) = (-1, 6)\)
- \((x_2, y_2) = (5, -2)\)

Now substituting the coordinates into the formula:

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

Calculating the differences:

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

Now substitute these values into the distance formula:

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

Calculating the squares:

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

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

So, the correct response is:

**10**