To determine which polygon correctly shows the line segment \( \overline{AC} \) with a length of 2 cm, we can calculate the distance between points A and C for each option, using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- For option 1: A(2,5), C(1,2)
\[ d = \sqrt{(1 - 2)^2 + (2 - 5)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.16 \text{ cm} \]
- For option 2: A(2,4), C(2,2)
\[ d = \sqrt{(2 - 2)^2 + (2 - 4)^2} = \sqrt{0^2 + (-2)^2} = \sqrt{4} = 2 \text{ cm} \]
- For option 3: A(2,3), C(2,2)
\[ d = \sqrt{(2 - 2)^2 + (2 - 3)^2} = \sqrt{0^2 + (-1)^2} = \sqrt{1} = 1 \text{ cm} \]
Thus, the option that correctly shows \( \overline{AC} \) having a length of 2 cm is option 2: A(2,4), C(2,2).