Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.
To apply the Pythagorean Theorem, we need to find the distance between the two points on a coordinate plane.
Let's label the coordinates of the first point as (x1, y1) and the coordinates of the second point as (x2, y2).
In this case, (x1, y1) = (-1, 6) and (x2, y2) = (5, -2).
The formula to find the distance between two points is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, we get:
d = √((5 - (-1))^2 + (-2 - 6)^2)
Simplifying:
d = √((5 + 1)^2 + (-2 - 6)^2)
d = √(6^2 + (-8)^2)
d = √(36 + 64)
d = √100
d = 10
The length between (-1, 6) and (5, -2) is 10 units.