Question

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

Explanation:

1. First, analyze the transformation from figure ③ to figure ①: A reflection (flip) over a vertical or horizontal line would align the orientation, then a translation (slide) to move it to the position of ①. Alternatively, check the other options. If we consider figure ② to ③ or ①, but the key is the combination. Let's see the options:

• Option 1: translation then rotation – the orientation change (from ② to ③ or ③ to ①) doesn't look like rotation after translation.
• Option 2: translation then reflection – no, the order might be wrong.
• Option 3: reflection then translation – Let's check: Reflect figure ② (or ③) first to get the orientation of ③ (or ①), then translate (slide) to the new position. This fits.
• Option 4: reflection then rotation – the final figure's orientation doesn't suggest rotation after reflection. So the correct combination is reflection, then translation.

Answer:

reflection, then translation