Question

Apply the Pythagorean
Theorem to find the length
between and
. Round your
answer to the nearest
hundredth, if necessary.
(1 point)
(−1, 6)
(5, − 2)
9.22
100
14
10

Answer 1

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

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

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

Now we can apply the Pythagorean Theorem:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the differences we calculated:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
Calculating the squares:
\[
d = \sqrt{36 + 64} = \sqrt{100}
\]
Taking the square root:
\[
d = 10
\]

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