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

rotation and dilation
reflection and translation
dilation and reflection
translation and dilation

Answer 1

To identify the sequence of transformations that exhibit the similarity between Figure 1 and Figure 2, we need to analyze the positions and orientations of the two trapezoids based on the descriptions provided.

1. Figure 1 is described as being larger and positioned in the grid with specific coordinates for its vertices.
2. Figure 2, a smaller trapezoid, is described as a mirror image of Figure 1 and positioned in a different part of the grid.

Analysis of the Transformations:

• Reflection: Figure 2 is a mirror image of Figure 1. This indicates that a reflection is involved, as the shapes are not just rotated or shifted but flipped over a line (in this case, likely along a vertical axis).

• Dilation: The fact that Figure 2 is a smaller version of Figure 1 suggests that a dilation (scaling down) has occurred in addition to reflection. Dilation modifies the size of the shape while maintaining the proportions (angles and the similarity of the shape) relative to the original figure.

Conclusion:

Given the analysis, the correct sequence of transformations that demonstrates the similarity between Figure 1 and Figure 2 is:

dilation and reflection.