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 10 10 14 14 100 100 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 derived from it:

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

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

Now, calculate the differences:

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

Now, plug these values into the distance formula:

\[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]

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