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

29
29

4.58
4.58

5.39
5.39

2.65

Answer 1

To find the distance between the points (2, 5) and (7, 3) using the Pythagorean Theorem, we can apply the distance formula, which is derived from the theorem. The distance formula is:

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

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

Now, we can calculate the differences in the coordinates:

\[
x_2 - x_1 = 7 - 2 = 5
\]
\[
y_2 - y_1 = 3 - 5 = -2
\]

Next, we can plug these values into the distance formula:

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

Calculating the squares:

\[
d = \sqrt{25 + 4}
\]

Now simplifying:

\[
d = \sqrt{29}
\]

Calculating the square root of 29:

\[
d \approx 5.385
\]

Rounding this to the nearest hundredth gives:

\[
d \approx 5.39
\]

So the answer is **5.39**.