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

5.39
5.39

2.65
2.65

4.58
4.58
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Answer 1

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

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

In this case:
- \( (x_1, y_1) = (2, 5) \)
- \( (x_2, y_2) = (7, 3) \)

Now substitute these into the distance formula:

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

Calculating the differences:

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

Calculating the squares:

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

Adding them together:

\[
d = \sqrt{29}
\]

Now, calculate the square root:

\[
d \approx 5.385
\]

Rounding to the nearest hundredth:

\[
d \approx 5.39
\]

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