Lines BC and DE are parallel to each other and the y-axis.  If the two lines were reflected across the y-axis and then the x-axis to form lines B'C' and D'E', which statement would be true about the lines B'C' and D'E'?

A. 

Lines B'C' and D'E' would be parallel to each other and the x-axis.

B. 

Lines B'C' and D'E' would no longer be parallel to each other.

C. 

Lines B'C' and D'E' would be parallel to each other and the y-axis.

D. 

Lines B'C' and D'E' would be perpendicular to each other.

1 answer

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.