This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes, indicating they point in the same direction: for example, y=2x+1 and y=2x+5 both have slope 2, so they are parallel and never intersect. Rigid transformations preserve these relationships by maintaining distances and angles, which define parallelism through equal corresponding angles with transversals. For instance, translating, reflecting, or rotating parallel lines keeps their directions consistent relative to each other. The best reason supporting the student's statement is that rigid transformations preserve distances and angles, including the 0° angle between parallel lines. A common error is claiming only translations preserve angles or that transformations change slopes, but all rigid ones preserve parallelism. To verify the property, note that parallelism relies on unchanged directional angles, which rigid transformations maintain universally; mistakes include confusing parallelism with constant distance, but it's about direction.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes, indicating they point in the same direction: for example, y=2x+1 and y=2x+5 both have slope 2, so they are parallel and never intersect. Rigid transformations like 180° rotations preserve slope relationships: horizontal lines remain horizontal with slope 0 after rotation, staying parallel. For instance, y=5 becomes y=-5 and y=-2 becomes y=2, both still horizontal and parallel. The correct statement is that l1' and l2' are still parallel because rotation preserves the angle between the lines. A common error is thinking rotations reverse directions or make lines perpendicular, but rigid transformations maintain parallelism. To verify, confirm initial parallelism (both slope 0), apply the rotation to negate coordinates equally, and check images are parallel horizontals; this property ensures no intersection is introduced.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes, indicating they point in the same direction: for example, y=2x+1 and y=2x+5 both have slope 2, so they are parallel and never intersect. Rigid transformations like reflections preserve slope relationships: reflecting y=3 and y=7 over the x-axis gives y=-3 and y=-7, both still with slope 0, so they remain parallel. For instance, points on l1 like (0,3) reflect to (0,-3) on y=-3, and similarly for l2, showing the image lines stay horizontal and parallel. The correct statement is that l1' and l2' are still parallel because both image lines are horizontal. A common error is claiming reflections change slopes to make lines perpendicular or intersecting, but all rigid transformations preserve parallelism. To verify, confirm the lines are initially parallel (both slope 0), apply the reflection to flip y-coordinates while keeping slopes zero, and check that image slopes are equal; this property holds because rigid transformations preserve angles, ensuring parallel relationships remain intact.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes, indicating they point in the same direction: for example, y=2x+1 and y=2x+5 both have slope 2, so they are parallel and never intersect. Rigid transformations like translations preserve slope relationships: shifting up by 9 units keeps both slopes at -1 without change. For instance, the image equations are y=-x+11 and y=-x+3, both with slope -1, showing preserved parallelism. The correct answer is that both slopes are -1. A common error is miscalculating post-translation slopes as changed or unequal, but translations never alter slopes. To verify, confirm initial slopes are -1, apply the vertical shift which only affects y-intercepts, and check images have identical slopes; this preservation stems from rigid transformations maintaining line directions.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): y=-(1/2)x+4 and y=-(1/2)x-1 both have slope -1/2 so parallel (never intersect). Rigid transformations preserve slope relationships: rotating both 90° counterclockwise changes slopes to 2 for both (still equal, still parallel). Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, a direction vector (2,-1) for slope -1/2 rotates to (1,2) for slope 2, and both lines get the same new slope, remaining parallel. The correct statement is that they are still parallel because rotation preserves angles and direction relationships. A common error is assuming rotation makes parallel lines perpendicular, but only perpendicular lines become something else; parallels stay parallel.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): all three have slope 3/4 so parallel (never intersect). Rigid transformations preserve slope relationships: reflecting across x-axis changes slopes to -3/4 for all (still equal, still parallel). Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, y=(3/4)x+1 becomes y=-(3/4)x-1 after reflection, and similarly for others, all with slope -3/4, remaining parallel. The correct description is that all three image lines are still parallel. A common error is thinking reflection changes slopes by different amounts, but it uniformly negates them while preserving equality.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): for example, y=2x+1 and y=2x+5 both slope 2 so parallel (never intersect). Rigid transformations preserve slope relationships: they maintain angles, including the directional alignment of parallels. Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, with specific parallel lines, applying a reflection shows slopes either stay the same or change equally, keeping them parallel. The best reason is that rigid transformations preserve angle measures, including the 0° angle between parallel lines. A common error is confusing parallelism with constant distance, but parallelism is about direction, preserved by rigid motions.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): vertical lines x=-2 and x=5 have undefined slope but are parallel (never intersect). Rigid transformations preserve slope relationships: rotating 180° about origin gives x=2 and x=-5 (still vertical, still parallel). Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, points on x=-2 like (-2,0) rotate to (2,0), and on x=5 like (5,0) to (-5,0), resulting in vertical lines x=2 and x=-5 that remain parallel. The correct equations are x=2 and x=-5, and they are still parallel. A common error is assuming rotation makes vertical lines horizontal or intersecting, but 180° rotation inverts positions while keeping them vertical.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): for example, y=2x+1 and y=2x+5 both slope 2 so parallel (never intersect). Rigid transformations preserve slope relationships: they maintain angles, including the directional alignment of parallels. Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, with specific parallel lines, applying a reflection shows slopes either stay the same or change equally, keeping them parallel. The best reason is that rigid transformations preserve angle measures, including the 0° angle between parallel lines. A common error is confusing parallelism with constant distance, but parallelism is about direction, preserved by rigid motions.

This question tests understanding that rotations, reflections, and translations preserve parallel lines—if two lines are parallel before the transformation, their image lines remain parallel after. Parallel lines have equal slopes (same direction): vertical lines x=-2 and x=5 have undefined slope but are parallel (never intersect). Rigid transformations preserve slope relationships: rotating 180° about origin gives x=2 and x=-5 (still vertical, still parallel). Reflection/rotation preserve parallelism similarly—parallel relationship (same angle with any transversal, equal slopes) maintains after any rigid transformation. For example, points on x=-2 like (-2,0) rotate to (2,0), and on x=5 like (5,0) to (-5,0), resulting in vertical lines x=2 and x=-5 that remain parallel. The correct equations are x=2 and x=-5, and they are still parallel. A common error is assuming rotation makes vertical lines horizontal or intersecting, but 180° rotation inverts positions while keeping them vertical.