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)

Question

Responses

100
100

14
14

10
10

9.22

Answer 1

To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we can use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \((x_1, y_1) = (-1, 6)\) and \((x_2, y_2) = (5, -2)\).

1. Calculate the differences:

   • \(x_2 - x_1 = 5 - (-1) = 5 + 1 = 6\)
   • \(y_2 - y_1 = -2 - 6 = -8\)

2. Substitute these values into the distance formula: \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]

Thus, the distance between the two points is \(10\).

The answer rounded to the nearest hundredth is still \(10.00\), but from the provided responses, the closest match is 10.