Question

Distance and the Pythagorean Theorem Quick Check
2 of 52 of 5 Items



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

2.65
2.65

29
29

5.39
5.39

4.58

Answer 1

To find the distance between the points (2, 5) and (7, 3), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

For the points (2, 5) and (7, 3):

- \(x_1 = 2\)
- \(y_1 = 5\)
- \(x_2 = 7\)
- \(y_2 = 3\)

Now, plug in 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, let's calculate \(\sqrt{29}\):

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

When rounding to the nearest hundredth, we get:

\[
d \approx 5.39
\]

Therefore, the correct response is:

**5.39**