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.

reflection and dilation

rotation and translation

rotation and dilation

translation and reflection

Answer 1

To determine the sequence of transformations that exhibits the similarity between Figures 1 and 2, let's analyze their placements and dimensions based on your description.

1. **Figure 1** is located from the top of the 3rd row to the bottom of the 3rd row (covering one row) and spans from the 3rd column to the 5th column (covering three columns).
2. **Figure 2** is located from the top of the 6th row to the bottom of the 8th row (covering three rows) and spans from the 7th column to the 7th column (covering one column).

Now, we are looking for transformations to make these two figures similar. The key concept of similarity involves maintaining the shape and proportions between figures through transformations such as translation, rotation, reflection, or dilation.

- **Translation** is moving an object without changing its size or shape.
- **Rotation** involves turning the object around a point.
- **Reflection** flips the object over a line.
- **Dilation** changes the size of the object but keeps its shape the same.

Given that Figures 1 and 2 are not in the same orientation, a **reflection** combined with a **dilation** could achieve similarity by flipping the shapes and adjusting the size.

Thus, the correct answer is:

**reflection and dilation**.