Question

Question
Apply the Pythagorean Theorem to find the length between (2, 5)
and (7, 3)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

29
29

4.58
4.58

2.65
2.65

5.39

Answer 1

To find the length between the points \( (2, 5) \) and \( (7, 3) \), we can use the distance formula, which is derived from the Pythagorean Theorem:

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

Here, let \( (x_1, y_1) = (2, 5) \) and \( (x_2, y_2) = (7, 3) \).

Now, substitute the values into the formula:

\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
\[
d = \sqrt{(5)^2 + (-2)^2}
\]
\[
d = \sqrt{25 + 4}
\]
\[
d = \sqrt{29}
\]

Now, we can calculate \( \sqrt{29} \):

\[
\sqrt{29} \approx 5.385
\]

Rounding this to the nearest hundredth gives:

\[
d \approx 5.39
\]

Thus, the length between the points \( (2, 5) \) and \( (7, 3) \) is approximately **5.39**.