Use the image to answer the question.

Question

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.

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 dilation
rotation and dilation

reflection and dilation
reflection and dilation

rotation and translation
rotation and translation
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Answer 1

To determine the transformations that exhibit the similarity between Figures 1 and 2, we need to analyze their positions and sizes.

1. Translation - This transformation involves moving the figure without altering its shape or size. If we can move Figure 1 to the position of Figure 2 without resizing it, we would have a translation.

2. Reflection - This involves flipping a figure over a line, which does not change its size but alters its orientation.

3. Rotation - This requires turning the figure around a specific point, which again does not change size but changes orientation.

4. Dilation - This transformation involves resizing a figure while maintaining its shape.

From the description:

• Figure 1 occupies rows 3 and columns 3-5.
• Figure 2 occupies rows 6-8 and column 7.

In this case, the most direct transformation to move from Figure 1’s location to Figure 2’s would be a translation down by 3 rows, but there is no need for any other transformation since they are the same size and shape.

Thus, the best answer is:

translation and reflection.

Note: Since the options suggest two transformations, let's also consider that if you need to transform the figures in a way that accommodates their specific arrangements, translating may imply some reflection across an axial line in their arrangement. However, primarily they remain similar by the properties of translation and, if needed, reflection across a center line.