Question

Find the distance between the points (9,1) and (8,5).
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 \( (9, 1) \) and \( (8, 5) \), we can use the distance formula:

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

Here, \( (x_1, y_1) = (9, 1) \) and \( (x_2, y_2) = (8, 5) \).

Substituting in the coordinates:

\[
d = \sqrt{(8 - 9)^2 + (5 - 1)^2}
\]

Calculating the differences:

\[
d = \sqrt{(-1)^2 + (4)^2}
\]

Calculating the squares:

\[
d = \sqrt{1 + 16}
\]

Adding the results:

\[
d = \sqrt{17}
\]

Thus, the distance between the points \( (9, 1) \) and \( (8, 5) \) is

\[
\boxed{\sqrt{17}}
\]