Question

Distance and the Pythagorean Theorem Quick Check
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

14
14

9.22
9.22

10
10

100

Answer 1

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

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

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

Now, we can substitute the coordinates into the formula:

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

This simplifies to:

\[
d = \sqrt{(5 + 1)^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

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

The correct answer is **10**.