Question

these figures are congruent. what series of transformations moves pentagon fghij onto pentagon fghij?
note: rotations are clockwise. reflections are over the x - or y - axis.
rotation, reflection
translation, translation
translation, reflection
reflection, translation

Explanation:

To determine the transformation series, we analyze the positions and orientations of the two pentagons. First, a rotation (e.g., 180 - degree rotation) can align the orientation, then a reflection (over an axis) and/or translation. But looking at the options, the correct series involves rotation, reflection, and then translation? Wait, no—wait, the correct option here is "Rotation, reflection" or let's re - examine. Wait, the two pentagons: one is in the upper right, one in the lower left. A rotation (like 180 degrees around the origin) would change the orientation, then a reflection? Wait, no, the correct option among the given is "Rotation, reflection" (the first option). Wait, let's check the coordinates. The original pentagon FGH IJ and the image F'G'H'I'J'. First, a rotation (clockwise, maybe 180 degrees) to align the shape, then a reflection? Wait, the options are:

1. Rotation, reflection

1. Translation, translation

1. Translation, reflection

1. Reflection, translation

Wait, when we look at the two pentagons, the first step could be a rotation (to change the orientation) and then a reflection. So the correct option is the first one: Rotation, reflection.

Answer:

A. Rotation, reflection