Question

y
8
7-
6-
C
5-
4
3-
A
2-
1-
04
-5 -4 -3
-2 -1
0
1
2
3
4
5
6
7
8
-
Determine the length of AC¯¯¯¯¯¯¯¯
.

(1 point)
Responses

6.32
6.32

5
5

3.61
3.61

7.81

Answer 1

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**