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 100 100 14 14 10 10 9.22

Answer 1

To find the length between the two points \((-1, 6)\) and \((5, -2)\), we can use the distance formula derived from the Pythagorean theorem. The formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

In this case, the points are:
- \((x_1, y_1) = (-1, 6)\)
- \((x_2, y_2) = (5, -2)\)

Now we can substitute these values into the formula:

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

Calculating each part:

1. \(5 - (-1) = 5 + 1 = 6\)
2. \(-2 - 6 = -8\)

So we have:

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

Calculating the squares:

1. \(6^2 = 36\)
2. \((-8)^2 = 64\)

Now add these results:

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

Finally, we take the square root:

\[
d = 10
\]

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

The correct response is **10**.