To determine the congruence transformation used on triangle \( \triangle ABC \) that resulted in triangle \( \triangle DEF \), you need to analyze the sequence of transformations that will lead from one triangle to the other based on the given descriptions.
-
Rotation: If \( \triangle ABC \) is rotated \( -180^\circ \) (clockwise) or \( 180^\circ \) (counterclockwise), every point will end up being rotated to the opposite side of the origin. This transformation can change the orientation of the triangle.
-
Reflection: Reflecting across the y-axis will mirror points across that axis. This will also change the orientation of the triangle.
-
Translation: Shifting the triangle 2 units to the right and 2 units up will move every point in the triangle without changing its orientation or shape.
Now, based on the transformations listed in the responses:
- You should analyze each option to see if they describe a direct way to obtain \( \triangle DEF \) from \( \triangle ABC \).
Since I cannot visualize the specific triangles based on your question, I recommend checking whether the positions of the corresponding vertices of the triangles match after applying the transformations listed in the options.
For example, if you notice that \( \triangle DEF \) appears to be a direct shift and no change in the orientation is apparent, then translation is the key step.
If you find that you need to rotate \( \triangle ABC \) and then shift it, that may point to an option that starts with a rotation.
Ultimately, from your description of the options:
- If rotations or reflections were involved but you also needed to shift the triangle after that, you should choose those options that mention both transformations.
Without seeing the actual triangles, I can't give a definitive answer, but you can determine it by logically examining how each transformation affects the triangles' positions.