To find the distance between the points \( (2, 5) \) and \( (7, 3) \), we can use 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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, \( (x_1, y_1) = (2, 5) \) and \( (x_2, y_2) = (7, 3) \).
Substituting the coordinates into the formula, we get:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \]
Calculating inside the square root:
\[ d = \sqrt{(5)^2 + (-2)^2} \]
\[ d = \sqrt{25 + 4} \]
\[ d = \sqrt{29} \]
Now, let's calculate the square root of 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 \( 5.39 \).
The correct response is:
5.39