Question

Apply the Pythagorean Theorem to find the length between (−1, 6)
and (5, −2)
. Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the distance 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 the formula:

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

Let's assign the coordinates:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 5\)
- \(y_2 = -2\)

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

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

Calculating \(5 - (-1)\):

\[
5 + 1 = 6
\]

Calculating \(-2 - 6\):

\[
-2 - 6 = -8
\]

Now substituting these values back into the formula, we have:

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

Calculating \(6^2\) and \((-8)^2\):

\[
6^2 = 36
\]
\[
(-8)^2 = 64
\]

Now summing these:

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

Finally, taking the square root gives us:

\[
d = 10
\]

Thus, the distance between the points \((-1, 6)\) and \( (5, -2)\) is \(10\). Rounding is not necessary here as it is a whole number.

**Final Answer: 10**