An illustration shows 2 trapezoids labeled Figure 1 and Figure 2 placed on a 12 column by 6 row grid. Figure 2 is smaller and a mirror image of Figure 1. Figure 1 shows the top left vertex on the top of the 3rd row and the start of the 3rd column, the top right vertex is on the top of the 3rd row and the start of the 5th column, the bottom left vertex is on the bottom of the 4th row and the start of 3rd column, and the bottom right vertex is on the bottom of the 4th row and the end of the 5th column. Figure 2 shows the top left vertex on the middle of the 3rd row and the middle of the 9th column, the top right vertex on the middle of the 3rd row and the end of the 10th column, the bottom left vertex on the end of the 4th row and on the 8th column, and the bottom right vertex on the end of the 4th row and end of the 10th column.

Question

Describe the sequence of transformations that exhibits the similarity between Figures 1 and 2.

(1 point)
Responses

reflection and translation
reflection and translation

dilation and reflection
dilation and reflection

rotation and dilation
rotation and dilation

translation and dilation

Answer 1

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, let's analyze the position and dimensions of each trapezoid based on the provided descriptions.

1. Reflection: Figure 2 is described as a mirror image of Figure 1. This indicates that a reflection transformation is involved. Since Figure 2 is on the right side of Figure 1, it suggests a reflection over a vertical axis (in this case, the vertical line between the two trapezoids).

2. Dilation: Figure 2 is described as smaller than Figure 1, which indicates that a dilation (scaling down) transformation has occurred.

Combining these transformations:

• First, Figure 1 underwent a dilation to become smaller.
• After this, it was reflected to create Figure 2.

Thus, the correct sequence of transformations that exhibits the similarity between Figures 1 and 2 is:

dilation and reflection.