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. 10
2. 9.22
3. 100
4. 14

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:

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

Plugging in the coordinates of the points:

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

We first calculate the differences:

\[
x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]
\[
y_2 - y_1 = -2 - 6 = -8
\]

Now, we can plug these values into the distance formula:

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

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

So the answer is **1. 10**.