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)

9.22

100

14

10

Answer 1

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

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

In this case, we have:

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

Substituting in the values:

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

Calculating the differences:

\[
d = \sqrt{(5 + 1)^2 + (2 - 6)^2} = \sqrt{(6)^2 + (-4)^2}
\]

Calculating the squares:

\[
d = \sqrt{36 + 16} = \sqrt{52}
\]

Now simplifying \(\sqrt{52}\):

\[
d = \sqrt{4 \times 13} = 2\sqrt{13}
\]

Now, we need to calculate \(2\sqrt{13}\) to get its decimal value. Using a calculator:

\(\sqrt{13} \approx 3.60555\)

Thus,

\[
d \approx 2 \times 3.60555 \approx 7.2111
\]

Rounding to the nearest hundredth gives us:

\[
d \approx 7.21
\]

This value does not match any of the given options exactly, but it seems like there might be a misunderstanding or a transcription error in the problem options since none of the provided distances (9.22, 100, 14, 10) are correct according to our calculation. Please double-check the provided options or the statements of the points.