Question

what combination of transformations is shown below?
options:
translation, then rotation
translation, then reflection
rotation, then translation
rotation, then reflection

Explanation:

1. Compare shape 1 and 2: Shape 2 is a mirror image of shape 1 across a vertical line, which is a reflection.
2. Compare shape 2 and 3: Shape 3 is shifted down and left from shape 2 without changing orientation, which is a translation.

Reversing the order, shape 1 is first reflected to get shape 2, then translated to get shape 3. Alternatively, analyzing shape 1 to 3 directly: shape 1 can be rotated to match the orientation of shape 3, then translated down/left. The rotation aligns the angle of the triangle, and the translation moves it to the final position, which matches the option.

Answer:

rotation, then translation