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
29
2.65
5.39

Answer 1

To find the length between the points \((2, 5)\) and \((7, 3)\), we can use the Pythagorean theorem, which is formulated as:

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

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

Now, let's calculate the differences:

\[
x_2 - x_1 = 7 - 2 = 5
\]
\[
y_2 - y_1 = 3 - 5 = -2
\]

Next, we square these differences:

\[
(x_2 - x_1)^2 = 5^2 = 25
\]
\[
(y_2 - y_1)^2 = (-2)^2 = 4
\]

Now, we can plug these values into the Pythagorean theorem:

\[
c = \sqrt{25 + 4} = \sqrt{29}
\]

Calculating \(\sqrt{29}\):

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

Rounding to the nearest hundredth, we get:

\[
5.39
\]

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