y

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

(1 point)
Responses

6.32
6.32

5
5

3.61
3.61

7.81

1 answer

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