How would you describe this series of transformations?

Question

(1 point)

1. Reflection across the y-axis and then a translation of (-3,-5) shows that triangle ABC is congruent to triangle A" B" C"

2. Since triangles ABC and A"B" C" do not have the same orientation, they are not congruent.

3. Rotation of 30 degrees clockwise and then reflection across the z-axis shows that triangle ABC is congruent to triangle A"B" C

4. Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A"B"C"

Answer 1

The series of transformations can be described as follows:

1. Transformation 1: Triangle ABC is first reflected across the y-axis, which changes its orientation, and then it is translated by the vector (-3, -5). This results in triangle A"B"C", but since the reflection has altered the orientation, the triangles ABC and A"B"C" are not congruent despite having the same shape and size.

2. Transformation 2: The statement reaffirms that triangles ABC and A"B"C" are not congruent due to the different orientations created by the reflection.

3. Transformation 3: Triangle ABC undergoes a rotation of 30 degrees clockwise, followed by a reflection across the z-axis. This transformation changes the triangle's position and orientation, but the resulting triangle A"B"C remains congruent to triangle ABC after the transformations are accounted for, implying that size and shape remain the same.

4. Transformation 4: Triangle ABC is then translated by the vector (2,0) and reflected across the x-axis. After these transformations, triangle A"B"C" is also congruent to triangle ABC, as translation and reflection preserve shape and size despite potentially altering orientation.

Overall, while different transformations may affect the orientation of triangles, congruence in terms of shape and size is maintained in some cases, specifically in transformations involving only translations and reflections.