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.395.392.652.654.584.5829

Answer 1

To find the length between the points \((2, 5)\) and \((7, 3)\), we will use the Pythagorean theorem. The formula to calculate the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Here, we have:
- \(x_1 = 2\)
- \(y_1 = 5\)
- \(x_2 = 7\)
- \(y_2 = 3\)

Now, substituting the values into the formula:

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

Calculating the differences:

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

Calculating the squares:

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

Now, adding the squares:

\[
d = \sqrt{29}
\]

Finally, calculating \(\sqrt{29}\):

\[
d \approx 5.385
\]

Rounded to the nearest hundredth, the distance is approximately:

\[
\boxed{5.39}
\]