Question

Find the distance between the points (-5, -8) and (0, 9).
Write your answer as a whole number or a fully simplified radical expression. Do not round.

Answer 1

To find the distance between the points \((-5, -8)\) and \((0, 9)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-5, -8)\) and \((x_2, y_2) = (0, 9)\).

Substituting the coordinates into the formula, we get:

\[
d = \sqrt{(0 - (-5))^2 + (9 - (-8))^2}
\]

Simplifying the expressions inside the parentheses:

\[
d = \sqrt{(0 + 5)^2 + (9 + 8)^2}
\]
\[
d = \sqrt{(5)^2 + (17)^2}
\]
\[
d = \sqrt{25 + 289}
\]
\[
d = \sqrt{314}
\]

The distance between the points \((-5, -8)\) and \((0, 9)\) is \(\sqrt{314}\). Since \(314\) does not have a perfect square factor besides \(1\), \(\sqrt{314}\) is already in its simplest form.

Thus, the final answer is:

\[
\sqrt{314}
\]