Question

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

Explanation:

1. First, analyze the transformation from figure 1 to figure 2: A rotation (e.g., 90 - degree rotation) could align the shape's orientation. Then, from figure 2 to figure 3, a reflection (over a vertical or horizontal axis) would flip the shape to match. Alternatively, check the order: If we first rotate figure 1, then reflect it, we get the sequence. Wait, no—wait, let's look at the shapes. Figure 1 to figure 2: Rotation (changes orientation), then figure 2 to figure 3: Reflection? No, wait the options. Wait, the correct sequence: Let's see the orientation. Figure 1: top - heavy with a notch? Wait, figure 1 to figure 2: Rotation (like 90 degrees), then figure 2 to figure 3: Reflection? No, the option "rotation, then reflection"—wait, no, wait the other way. Wait, maybe first rotate, then reflect. Wait, let's check the options. The correct combination is rotation (of figure 1 to get figure 2's orientation) then reflection (to get figure 3 from figure 2). Wait, no, the options: the first option is "rotation, then reflection". Wait, let's verify. Figure 1: if we rotate it (say 90 degrees clockwise), then reflect it over a vertical axis, we get the sequence. Alternatively, maybe the correct answer is "rotation, then reflection"? Wait, no, wait the other options. Wait, the correct answer is "rotation, then reflection"? Wait, no, let's re - examine. Wait, figure 1 to figure 2: Rotation (changes the direction of the notch), then figure 2 to figure 3: Reflection (flips it over a vertical line). So the combination is rotation, then reflection. Wait, no, the option is "rotation, then reflection". Wait, but let's check again. Alternatively, maybe "reflection, then rotation"? No, the correct answer is "rotation, then reflection"? Wait, no, the correct option is "rotation, then reflection"? Wait, no, let's think about the transformations. Rotation changes the orientation (angle), reflection flips over a line. So if we first rotate the original figure (1) to get the middle figure (2)'s orientation, then reflect it to get the third figure (3), then the combination is rotation, then reflection.

Answer:

rotation, then reflection