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

5.39
5.39

29
29

4.58
4.58

2.65

Answer 1

To find the distance between the points \((2, 5)\) and \((7, 3)\) using the Pythagorean Theorem, we first calculate the differences in the x-coordinates and y-coordinates.

1. Calculate the difference in x-coordinates:
\[
\Delta x = 7 - 2 = 5
\]

2. Calculate the difference in y-coordinates:
\[
\Delta y = 3 - 5 = -2
\]

3. Use the Pythagorean Theorem to find the distance \(d\):
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

4. Calculate \(\sqrt{29}\):
\[
\sqrt{29} \approx 5.385
\]

Rounded to the nearest hundredth, this is approximately 5.39.

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