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

4.58
4.58

29
29

5.39
5.39

2.65

Answer 1

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

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

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

Now, we can plug in the values:

1. Calculate \(x_2 - x_1\):

\[
x_2 - x_1 = 7 - 2 = 5
\]

2. Calculate \(y_2 - y_1\):

\[
y_2 - y_1 = 3 - 5 = -2
\]

3. Now, plug these into the distance formula:

\[
d = \sqrt{(5)^2 + (-2)^2}
\]
\[
d = \sqrt{25 + 4}
\]
\[
d = \sqrt{29}
\]

Now, calculate \(\sqrt{29}\):

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

Rounding to the nearest hundredth:

\[
d \approx 5.39
\]

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