Final answer:
All sequences of transformations mentioned involve rigid motions (reflection, rotation, and translation) which preserve the size and shape of the original figure, resulting in congruent shapes after the transformations are applied.
Step-by-step explanation:
The student's question pertains to geometric transformations and congruency. To classify the given sequences of transformations as to whether they show congruence, we will consider the effects of reflections, rotations, and translations on a shape.
A transformation sequence that consists of reflections, rotations, and translations can still result in congruent shapes because these are all rigid motions. Rigid motions preserve distances and angles, which means the pre-image and image are congruent after the transformation.
- Reflection across the y-axis will result in a mirror image of the shape across the vertical line of the y-axis.
- A 90° counterclockwise or clockwise rotation will rotate the shape 90 degrees in the specified direction around the origin.
- A translation moves the shape in a straight line path without changing its size or orientation in the plane.
All of the given sequences consist of a reflection, a 90° rotation (either clockwise or counterclockwise), and a translation (either up or down, left or right). Since all these transformations are types of rigid motions, they will each result in a shape that is congruent to the original.
Therefore, whether the translation is 6 units down, 6 units up, or even 4 units down, the final shape after applying these transformations will be congruent to the initial shape. What changes is not the size or shape, but the position of the image in the plane.