Question

what combination of transformations is shown below?

(image of a grid with three polygons labeled 1, 2, 3)

options:

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

Explanation:

Step1: Analyze Transformation from 1 to 2

First, look at figure 1 and figure 2. A rotation (around a common vertex) would align figure 1 to figure 2's orientation. Then, from figure 2 to figure 3, a reflection (over a line of symmetry) would flip it to match figure 3's position and orientation. Wait, no—wait, let's re-examine. Wait, figure 1 to 2: rotation? Or figure 1 to 2: maybe rotation, then figure 2 to 3: reflection? Wait, no, the options: let's check the order. Wait, the correct combination: first, rotate figure 1 to get figure 2 (rotation), then reflect figure 2 to get figure 3 (reflection)? Wait, no, the options are rotation then reflection? Wait, no, let's check the figures. Figure 1 (blue) to figure 2 (light blue): rotation around the common vertex. Then figure 2 to figure 3 (purple): reflection over a vertical or horizontal line? Wait, no, the correct option is "rotation, then reflection"? Wait, no, let's check the options. The options are:

1. translation, then rotation

1. translation, then reflection

1. rotation, then translation

1. rotation, then reflection

Wait, when we look at figure 1 to figure 2: it's a rotation (around the shared vertex) to get from 1 to 2. Then from figure 2 to figure 3: a reflection (over a line) to get the purple figure. So the combination is rotation, then reflection.

Step2: Confirm the Transformations

First, rotate figure 1 to obtain figure 2 (rotation about a point). Then, reflect figure 2 to obtain figure 3 (reflection over a line). So the combination is rotation, then reflection.

Answer:

rotation, then reflection