Distance and the Pythagorean Theorem Quick Check

Question

3 of 53 of 5 Items

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

14
14

10
10

100

Answer 1

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

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

In this case, let \( (x_1, y_1) = (-1, 6) \) and \( (x_2, y_2) = (5, -2) \).

Now, substitute the coordinates into the formula:

\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \]

Calculating the differences:

\[ d = \sqrt{(5 + 1)^2 + (-2 - 6)^2} \] \[ d = \sqrt{(6)^2 + (-8)^2} \]

Now calculate the squares:

\[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]

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

So the correct response is:

10