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An illustration shows two squares labeled Figure 1 and Figure 2 placed on a 12 column by 10 row grid. Figure 2 is rotated on an angle and larger than Figure 1. Figure 1 extends from the top of the 3rd to the bottom of the 5th row and the start of the 2nd to the end of 4th columns. The sides extend for 2 units on each side of the grid. Figure 2 in inclined at an angle. The right vertex is in the 5th row in the 12th column. The bottom vertex is at the bottom of the 9th row between the 8th and 9th columns. The left vertex is in the 6th row in the 4th column. The top vertex is in the 1st row in the 7th column.

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

rotation and reflection

translation and reflection

translation and dilation

rotation and dilation

1 answer

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, let's analyze their positions and sizes based on the information provided:

  1. Figure 1 is located on the grid with its vertices defined by the rows (3rd to 5th row) and columns (2nd to 4th column). This indicates that it is a square placed in that grid with certain dimensions.

  2. Figure 2 is larger and rotated at an angle. Its vertices are given specific locations, and since it's larger than Figure 1, there must be a dilation in size.

To find the transformations between Figure 1 and Figure 2:

  • Dilation: Since Figure 2 is larger than Figure 1, a dilation (enlargement) from Figure 1 to Figure 2 is evident.

  • Rotation: Given that Figure 2 is described as rotated at an angle, it is clear that a rotation has occurred to align it with its current orientation compared to Figure 1.

  • Reflection and Translation: There is no indication of reflection since both figures maintain the same structural shape and orientation (besides rotation). Translation does not seem necessary as we are primarily discussing size changes and rotation.

Putting this all together, the transformations involved in exhibiting the similarity between the two figures would be:

Rotation and Dilation.

Thus, the correct answer is "rotation and dilation."