Use the image to answer the question.

Question

An illustration shows five triangles labeled Figure 1 through Figure 5 placed on a 14 column by 12 row grid. Figures 1, 2, 3, and 5 are all the same size. Figure 4 is slightly larger. Figure 1 shows the top vertex on the top of the 3rd row and the start of the 3rd column. The bottom vertex is on the bottom of the 5th row and the start of the 3rd column. The right vertex is between the 3rd and the 4th rows and the end of the 4th column. Figure 2 shows the left vertex between the 3rd and 4th rows and the start of the 9th column. The top vertex in on the top of the 3rd row and the end of the 10th column. The bottom vertex is on the bottom of the 5th row and the end of the 10th column. Figure 3 shows the base left vertex on the bottom of the 6th row and the start of the 5th column. The base right vertex is on the bottom of the 6th row and the end of the 7th column. The top vertex is on the top of the 5th row and between the 5th and 6th columns. Figure 4 shows the base left vertex on the end of the 10th row and in the middle of the 7th column. The base right vertex is on the bottom of the 10th row and the middle of the 13th column. The top vertex is on the beginning of the 7th row and the middle of the 9th column. Figure 5 shows the top vertex on top of the 8th row and the start of the 3rd column. The bottom vertex is on the bottom of the 10th row and the start of the 3rd column. The right vertex is between the 8th and 9th rows and the end of the 4th column.

Which figure would result from rotating and dilating Figure 1?

(1 point)
Responses

Figure 5
Figure 5

Figure 2
Figure 2

Figure 4
Figure 4

Figure 3

Answer 1

To determine which figure would result from rotating and dilating Figure 1, we need to analyze the positions and shapes of the figures described.

• Figure 1 is a triangle located with its top vertex at the 3rd row and 3rd column, with a base along the 5th row.

• Figure 5 has a top vertex at the 8th row and 3rd column, with its base down to the 10th row. The right vertex is positioned between the 8th and 9th rows and at the end of the 4th column.

To see if Figure 5 could result from transforming Figure 1, we need to consider that the top vertex of Figure 5 is at a different row level (8th row vs. 3rd row for Figure 1), while the base remains in the same column (3rd column). Rotating Figure 1 would change its orientation but would not maintain the same shape since its height has increased significantly.

• Figure 2 has a similar configuration as Figure 1 but shifted horizontally. The orientation could be altered via rotation but it is not a dilation.

• Figure 3 has a different structure and scaling than Figure 1.

• Figure 4 is larger but placed differently on the grid, deviating from the form of Figure 1.

Given this analysis, after considering how dilation changes a figure in size while maintaining proportions, Figure 5 does not reflect the transformation of Figure 1. Similarly, Figures 2, 3, and 4 also do not represent a dilation or rotation that can be directly associated with Figure 1.

Therefore, the best choice provided that relates to a rotation or dilation transformation of Figure 1 should logically lead to Figure 2, as it aligns closely with the properties of rotation and size change even within considerations of translation on the grid.

Correct Answer: Figure 2