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)

9.22

100

14

10

Answer 1

To find the length between the points \((-1, 6)\) and \( (5, -2)\) using the Pythagorean Theorem, we can treat the distance as the hypotenuse of a right triangle.

First, we need to find the differences in the x-coordinates and y-coordinates:

- The change in x (Δx) = \(5 - (-1) = 5 + 1 = 6\)
- The change in y (Δy) = \(-2 - 6 = -8\)

Now we can apply the Pythagorean Theorem:

\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

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

The correct answer is **10**.