Given that lines BC and DE are parallel to each other and the y-axis, we can denote these lines as having the equations \( x = k_1 \) and \( x = k_2 \), where \( k_1 \) and \( k_2 \) are constants representing the x-coordinates of lines BC and DE, respectively.
When these lines are reflected across the y-axis, their equations change as follows:
- Line BC becomes \( x = -k_1 \)
- Line DE becomes \( x = -k_2 \)
Since both lines are still vertical (parallel to the y-axis), they remain parallel to each other after this reflection.
Next, we reflect the lines across the x-axis:
- Reflecting \( x = -k_1 \) across the x-axis does not change its equation (as it remains vertical).
- Similarly for \( x = -k_2 \).
After both reflections, the lines \( B'C' \) and \( D'E' \) are still vertical lines, thus having the equations:
- Line B'C' is \( x = -k_1 \)
- Line D'E' is \( x = -k_2 \)
Since \( k_1 \) and \( k_2 \) are constants, and assuming \( k_1 \neq k_2 \), the lines remain parallel to each other and still vertical.
So the correct statement about lines B'C' and D'E' after the reflections is:
C. Lines B'C' and D'E' would be parallel to each other and the y-axis.