Question

Find the distance between the points (3,7) and (8,3).
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 \((3,7)\) and \((8,3)\), we can use the distance formula, which is given by:

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

In this case, we have:
- \( (x_1, y_1) = (3, 7) \)
- \( (x_2, y_2) = (8, 3) \)

Now we can plug in the coordinates into the distance formula:

\[
d = \sqrt{(8 - 3)^2 + (3 - 7)^2}
\]

Calculating the differences:

\[
8 - 3 = 5
\]
\[
3 - 7 = -4
\]

Substituting these values into the formula gives:

\[
d = \sqrt{(5)^2 + (-4)^2}
\]
\[
= \sqrt{25 + 16}
\]
\[
= \sqrt{41}
\]

Thus, the distance between the points \((3,7)\) and \((8,3)\) is:

\[
\boxed{\sqrt{41}}
\]