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 10 100 100 14 14 9.22

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:

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

Here, the coordinates are:
- \( (x_1, y_1) = (-1, 6) \)
- \( (x_2, y_2) = (5, -2) \)

Now, let's plug in the values:

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. Now, substitute these into the distance formula:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

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

The answer is \(10\).