Question

Find the distance between the points (8,8) and (9,0).
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 \((8,8)\) and \((9,0)\), we can use the distance formula, which is given by:

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

Here, the coordinates of the points are:
- \((x_1, y_1) = (8, 8)\)
- \((x_2, y_2) = (9, 0)\)

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

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

Calculating each term:

1. \(9 - 8 = 1\)
- Hence, \((9 - 8)^2 = 1^2 = 1\)

2. \(0 - 8 = -8\)
- Hence, \((0 - 8)^2 = (-8)^2 = 64\)

Now substituting these values back into the equation:

\[
d = \sqrt{1 + 64}
\]
\[
d = \sqrt{65}
\]

Since \(65\) is not a perfect square, we can leave our answer as:

\[
\boxed{\sqrt{65}}
\]