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

100
100

9.22

Answer 1

To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we first calculate the difference in the x-coordinates and the y-coordinates.

1. Calculate the difference in x-coordinates:
\[
\Delta x = x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]

2. Calculate the difference in y-coordinates:
\[
\Delta y = y_2 - y_1 = -2 - 6 = -8
\]

3. Use the Pythagorean Theorem to find the distance \(d\):
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(6)^2 + (-8)^2}
\]
\[
= \sqrt{36 + 64} = \sqrt{100} = 10
\]

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

The answer is:
**10**