Question

reflection, then rotation
reflection, then translation
translation, then reflection
translation, then rotation

Explanation:

Step1: Analyze the shapes

First, observe the orientation and position of shape ①, ②, and ③. Shape ① and ②: To get from ① to ②, we can first reflect ① over a vertical line (to make it face the same direction as ②'s base) and then translate (move) it to the left to align with ②. Wait, no, let's check again. Wait, shape ① and ②: Wait, maybe ① to ②: Wait, actually, looking at the positions, if we take shape ①, reflect it (over a vertical axis, maybe) so that its slant side matches ②'s slant side, then translate it left. Wait, no, the correct sequence: Let's see the options. The options are reflection then rotation, reflection then translation, translation then reflection, translation then rotation.

Wait, shape ① and ②: Let's see the orientation. Shape ① is a trapezoid with the slant side on the left? Wait, no, in the image, shape ① (purple) has the slant side on the left, shape ② (blue) has the slant side on the right? Wait, no, maybe I got it reversed. Wait, shape ① is on the right, purple, shape ② is on the left, blue, below shape ③ (tan). So to get from ① to ②: First, reflect ① over a vertical line (so that the slant side is on the right, matching ②'s slant side), then translate (move) it to the left to the position of ②. Alternatively, translation then reflection? Wait, no. Wait, let's think about the transformations. Reflection flips the shape, translation moves it, rotation turns it.

Wait, the correct answer: Let's check the options. The key is to see the transformation from ① to ② (or maybe ② to ①? Wait, no, the problem is probably about transforming ① to ② or ① to ③? Wait, the image has ① (purple), ② (blue), ③ (tan). Let's assume we need to transform ① to ②. So first, reflect ① over a vertical line (so that the slant side is on the right, like ②), then translate it left. So the sequence is reflection, then translation. Wait, but let's confirm. Alternatively, if we translate first, then reflect, would that work? No, because translation would move it, but the orientation is different. So the correct option is "reflection, then translation". Wait, no, maybe I made a mistake. Wait, let's look at the shapes again. Shape ① is a trapezoid with the left side slanting, shape ② is a trapezoid with the right side slanting. So to make ① look like ②, we need to reflect it over a vertical axis (so the slant side is on the right), then translate it to the left. So the transformation is reflection then translation.

Step2: Confirm the option

Looking at the options, the second option is "reflection, then translation". So that's the correct one.

Answer:

reflection, then translation