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

9.22
9.22

10
10

14
14

100

1 answer

To find the length between two points using the Pythagorean Theorem, we need to find the distance between the x-coordinates and the distance between the y-coordinates, and then apply the theorem.

Let's label the points as A(-1, 6) and B(5, -2).

The distance between the x-coordinates is: 5 - (-1) = 6.

The distance between the y-coordinates is: -2 - 6 = -8.

To find the distance between the two points, we can use the formula d = sqrt((Δx)^2 + (Δy)^2), where d is the distance, Δx is the difference in x-coordinates, and Δy is the difference in y-coordinates.

In this case, d = sqrt((6)^2 + (-8)^2).

d = sqrt(36 + 64) = sqrt(100) = 10.

The length between (-1, 6) and (5, -2) is 10.