<|system|>
Triangle $ABC$ with vertices $A(-2, 0)$, $B(1, 4)$ and $C(-3, 2)$ is reflected over the $y$-axis to form triangle $A'B'C'$. What is the length of a segment drawn from $C$ to $C'$?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
To reflect a point over the $y$-axis, I need to change the sign of its $x$-coordinate and keep the $y$-coordinate the same. So, the coordinates of $C'$ are $(3, 2)$. Now, to find the length of the segment from $C$ to $C'$, I can use the distance formula, which is based on the Pythagorean theorem. The distance formula says that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. In this case, I can plug in the coordinates of $C$ and $C'$ and simplify. The distance is $\sqrt{(3 - (-3))^2 + (2 - 2)^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6$. So, the length of the segment from $C$ to $C'$ is 6 units. 