Use the image to answer the question.

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

translation and reflection
translation and reflection

translation and dilation
translation and dilation

rotation and reflection
rotation and reflection

rotation and dilation

Answer 1

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, we can analyze their descriptions:

• Figure 1 is described as being a square that occupies a specific area in the grid.
• Figure 2 is larger and rotated at an angle, indicating a transformation that alters its orientation and size compared to Figure 1.

Since similarity in geometry often involves scaling (which is dilation) and possibly rotation to match shapes, we can conclude:

1. Dilation is involved because Figure 2 is larger than Figure 1.
2. Rotation is also involved because Figure 2 is inclined at an angle.

Thus, the sequence of transformations that shows the similarity between Figures 1 and 2 is rotation and dilation.

Therefore, the correct answer is:

rotation and dilation.