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)
Responses

9.22
9.22

10
10

100
100

14
14

Answer 1

To find the length between two points using the Pythagorean Theorem, we need to calculate the distance between the x-coordinates and the distance between the y-coordinates, and then use those distances to find the hypotenuse.

The distance between the x-coordinates is 5 - (-1) = 6 units.
The distance between the y-coordinates is -2 - 6 = -8 units.

To find the length between the two points, we can use the Pythagorean Theorem:

c^2 = a^2 + b^2

where c represents the hypotenuse and a and b represent the other two sides.

In this case:
c^2 = 6^2 + (-8)^2
c^2 = 36 + 64
c^2 = 100

Taking the square root of both sides, we find:
c = √100
c = 10

Therefore, rounding to the nearest hundredth, the length between the two points is approximately 10 units.