To find the length between the points (2, 5) and (7, 3), we can use the Pythagorean Theorem, which states that:
\[ c = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).
Now, we'll calculate the differences in the x and y coordinates:
\[ x_2 - x_1 = 7 - 2 = 5 \]
\[ y_2 - y_1 = 3 - 5 = -2 \]
Now we can plug these values into the formula:
\[ c = \sqrt{(5)^2 + (-2)^2} \]
Calculating the squares:
\[ (5)^2 = 25 \]
\[ (-2)^2 = 4 \]
Now add these together:
\[ c = \sqrt{25 + 4} = \sqrt{29} \]
Finally, calculating \(\sqrt{29}\):
\[ c \approx 5.385 \]
Rounding to the nearest hundredth gives us:
\[ c \approx 5.39 \]
So, the length between the points (2, 5) and (7, 3) is 5.39.
The correct answer is 4. 5.39.