Rigid Motions and Transformations

This lesson covers sequencing reflections and translations, emphasizing that reflections are their own inverse. It explains how reflecting a point twice across the same line returns it to its original position. The lesson also highlights the importance of the order of transformations, showing that different sequences can lead to different outcomes. Exercises are provided to reinforce these concepts, and the lesson concludes with a summary of key points.

What is the inverse of a translation along a vector?

• Translation along the same vector

• Translation along the opposite vector

• Reflection across a line

• Rotation around a point

What happens when a figure is reflected across a line and then reflected again across the same line?

• The figure rotates 90 degrees

• The figure is translated along a vector

• The figure returns to its original position

• The figure moves to a new position

If a point is not on the line of reflection, what is the result of reflecting it twice across the same line?

• The point returns to its original position

• The point remains unchanged

• The point is rotated 180 degrees

• The point moves to a new location

What is the result of reflecting a point on the line of reflection twice?

• The point returns to its original position

• The point remains unchanged

• The point moves to a new location

• The point is translated along a vector

Does the order of performing a reflection and a translation affect the final position of a figure?

• Yes, the order affects the final position

• No, the order does not matter

• Only if the figure is a polygon

• Only if the figure is a circle

What is the result of performing a translation followed by a reflection?

• The figure is rotated 90 degrees

• The figure returns to its original position

• The figure is unchanged

• The figure moves to a new position

What is the identity transformation in the context of reflections?

• A transformation that leaves the figure unchanged

• A transformation that changes the figure

• A transformation that rotates the figure

• A transformation that translates the figure

What is the effect of performing a reflection followed by a translation on a figure?

• The figure is unchanged

• The figure is rotated 180 degrees

• The figure moves to a new position

• The figure returns to its original position

What is the significance of the order in which rigid motions are performed?

• The order only matters for translations

• The order affects the final position

• The order does not affect the final position

• The order only matters for reflections

Which of the following is true about a reflection?

• It is not its own inverse

• It is its own inverse

• It is always followed by a rotation

• It is always followed by a translation