An illustration shows two rectangles of the same size and shape labeled Figure 1 and Figure 2 placed on a 9 column by 10 row grid. Figure 1 extends from the top of the 3rd row to the bottom of the 3rd row and the start of the 3rd column to the end of the 5th column. Figure 2 extends from the top of the 6th row to the bottom of the 8th row and the start of the 7th column to the end of the 7th column.

Question

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

(1 point)
Responses

translation and reflection
translation and reflection

rotation and translation
rotation and translation

reflection and dilation
reflection and dilation

rotation and dilation

Answer 1

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, we need to analyze the positions and orientations of the rectangles.

• Figure 1 is located in rows 3 and spans from column 3 to column 5.
• Figure 2 is located in rows 6 to 8 and occupies only column 7.

Given this information, we can deduce the following:

1. Translation: Figure 1 can be translated downwards from its position (in row 3) to row 6 where Figure 2 starts, moving 3 rows down.
2. Reflection: Since the two rectangles are oriented differently, with Figure 1 being horizontal and Figure 2 appearing in a vertical position, we can consider that a reflection across a vertical line (or possibly a horizontal line if we think in terms of flipping the rectangle) is involved.

However, note that Figure 2 appears to be solely vertical; if the size is identical and it retains proportions but changes orientation, the simpler explanation is the transformation has both reflection across a vertical axis and dilation in relation to width compared to height (keeping ratios).

Thus, the correct sequence of transformations that maintains similarity while taking into account their orientations and positions would be:

Reflection and dilation.

Therefore, the answer is:

reflection and dilation.