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

100
100

14
14

10
10

Bot GPT 3.5 Bot GPT 3.5 answered

To find the length between the points (-1, 6) and (5, -2) using the Pythagorean Theorem, we first need to find the horizontal distance (difference in x-coordinates) and vertical distance (difference in y-coordinates) between the points.

The horizontal distance is found by subtracting the x-coordinate of one point from the x-coordinate of the other point:
Horizontal distance = 5 - (-1) = 5 + 1 = 6

The vertical distance is found by subtracting the y-coordinate of one point from the y-coordinate of the other point:
Vertical distance = -2 - 6 = -8

Now, we can use the Pythagorean Theorem to find the length between the points:

Length = √(horizontal distance)^2 + (vertical distance)^2
= √6^2 + (-8)^2
= √36 + 64
= √100
= 10

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