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.

Question

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

Answer 1

To identify the sequence of transformations that exhibit the similarity between Figure 1 and Figure 2, let's analyze the given information:

1. Properties of Figure 1:

   • It occupies specific rows and columns in the grid, fitting exactly within a defined area.
   • The dimensions are consistent since it's a square, meaning its angles are right angles and all sides are of equal length.

2. Properties of Figure 2:

   • It is larger than Figure 1 and is rotated at an angle (inclined).
   • The vertices are defined, indicating that it maintains the properties of a square even if the orientation is different.

Given that Figure 2 is larger than Figure 1 yet maintains the same shape (both being squares), we can infer that a dilation is required. Furthermore, the fact that Figure 2 is rotated suggests that there is also a rotation transformation involved.

Reflecting on the options provided, "rotation and dilation" aligns perfectly with the observed transformations, as it accurately describes the relationship between the two figures:

• Rotation accounts for the change in orientation,
• Dilation accounts for the increase in size.

Thus, the correct choice from the options listed is:

rotation and dilation.