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Question

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.

(1 point)
Responses

rotation and dilation
rotation and dilation

translation and reflection
translation and reflection

translation and dilation
translation and dilation

rotation and reflection
rotation and reflection
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Answer 1

To describe the similarity between Figures 1 and 2, we need to consider the characteristics of each figure based on the information provided:

1. Similar Shape: Both figures are squares. They maintain the same shape but have different sizes.

2. Transformations: The transformations that can be applied to one figure to make it similar to the other typically include rotation, translation, and dilation (resizing).

Analyzing the Transformations:

• Rotation: Figure 2 is rotated compared to Figure 1. Since Figure 2 is inclined at an angle, this transformation is necessary.

• Dilation: Figure 2 is larger than Figure 1. Dilation indicates that Figure 2 has been stretched or enlarged from Figure 1 while keeping the shape the same.

Therefore, the correct transformation sequence that exhibits similarity between Figures 1 and 2 is:

rotation and dilation.

This is the appropriate response as it encompasses both the rotation and the size difference between the two figures.