Understand Parallel Line Transformation Properties Practice Test

Two parallel lines are each transformed by the same sequence: a reflection across the $$y$$-axis, followed by a translation of 3 units up, followed by a $$180°$$ rotation about point $$(2, -1)$$. A student argues that since each line undergoes the exact same transformations, the lines might not remain parallel because $$180°$$ rotations can change parallel lines into intersecting lines. Evaluate this argument.

In quadrilateral $$EFGH$$, side $$\overline{EF}$$ is parallel to side $$\overline{HG}$$, but side $$\overline{EH}$$ is not parallel to side $$\overline{FG}$$. After applying a rotation of $$120°$$ about point $$P$$, followed by a reflection across line $$m$$, what is true about the parallel relationships in the transformed quadrilateral?