Question

Apply the Pythagorean Theorem to find the length between (2, 5)
(
2
,

5
)
and (7, 3)
(
7
,

3
)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

2.65
2.65

4.58
4.58

29
29

5.39

Answer 1

The Pythagorean Theorem is used to find the distance between two points in a coordinate plane. The formula for the distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Given the points \( (2, 5) \) and \( (7, 3) \):

1. Identify the coordinates:
- \( (x_1, y_1) = (2, 5) \)
- \( (x_2, y_2) = (7, 3) \)

2. Plug in the coordinates into the distance formula:
\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
\[
= \sqrt{(5)^2 + (-2)^2}
\]
\[
= \sqrt{25 + 4}
\]
\[
= \sqrt{29}
\]

3. Now calculate \( \sqrt{29} \):
\[
\sqrt{29} \approx 5.385
\]

4. Rounding to the nearest hundredth, we get:
\[
d \approx 5.39
\]

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