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 2.65 2.65 4.58 4.58 5.39

Answer 1

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

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

Substituting the coordinates of the points:

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

Now, calculate the differences:

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

Next, plug these values into the distance formula:

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

Calculating \(\sqrt{29}\):

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

Rounding to the nearest hundredth gives us approximately \(5.39\).

Thus, the distance between the points \((2, 5)\) and \((7, 3)\) is \( \boxed{5.39} \).