Distance and the Pythagorean Theorem Quick Check

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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

1 answer

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.