To determine the length of segment \( \overline{AC} \), we first need the coordinates of points \( A \) and \( C \).
By the provided graph coordinates:
- Point \( A \) appears to be at (0, 4).
- Point \( C \) appears to be at (-3, 6).
Using the distance formula to calculate the length of segment \( \overline{AC} \):
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of points \( A \) and \( C \):
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (-3, 6) \)
\[ d = \sqrt{((-3) - 0)^2 + (6 - 4)^2} \]
This simplifies to:
\[ d = \sqrt{(-3)^2 + (2)^2} \] \[ d = \sqrt{9 + 4} \] \[ d = \sqrt{13} \] \[ d \approx 3.61 \]
Thus, the length of segment \( \overline{AC} \) is approximately \( 3.61 \).
Therefore, the correct response is:
3.61