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 \((5, -2)\) using the Pythagorean Theorem, we first need to determine the differences in the \(x\) and \(y\) coordinates:

- The difference in the \(x\) coordinates:
\[
x_2 - x_1 = 5 - (-1) = 5 + 1 = 6
\]

- The difference in the \(y\) coordinates:
\[
y_2 - y_1 = -2 - 6 = -8
\]

Now, we can use the distance formula, which is derived from the Pythagorean Theorem:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the differences we calculated:
\[
d = \sqrt{(6)^2 + (-8)^2}
\]
Calculating the squares:
\[
d = \sqrt{36 + 64}
\]
Adding the squares:
\[
d = \sqrt{100}
\]
Taking the square root:
\[
d = 10
\]

Thus, the distance between the points \((-1, 6)\) and \((5, -2)\) is \(10\). Since we were asked to round to the nearest hundredth, the final answer is:

\[
\boxed{10.00}
\]