Similar Figures Quick Check

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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.

(1 point)
Responses

rotation and reflection
rotation and reflection

translation and reflection
translation and reflection

rotation and dilation
rotation and dilation

translation and dilation
translation and dilation
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Answer 1

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, we need to analyze their characteristics:

1. Figure 1 is a square that is positioned in a standard orientation.
2. Figure 2, while described as a square as well, is rotated at an angle and larger than Figure 1.

To show that Figure 2 is similar to Figure 1:

• Rotation is needed because Figure 2 is inclined at an angle compared to the aligned orientation of Figure 1.
• Dilation is necessary because Figure 2 is larger than Figure 1.

The transformations that maintain the shape but change the size and orientation of the figure are rotation and dilation.

Therefore, the correct response is:

rotation and dilation.