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 2
Figure 2

Figure 5
Figure 5

Figure 4
Figure 4

Figure 3

Answer 1

To determine which figure would result from rotating and dilating Figure 1, let's first summarize the position of the vertices for Figure 1:

• Top vertex: 3rd row, 3rd column
• Bottom vertex: 5th row, 3rd column
• Right vertex: between 3rd and 4th rows, end of 4th column

Figure 1 is an upright triangle located in the left section of the grid.

Now let's analyze the other figures:

• Figure 2: The top vertex is at the 3rd row, end of the 10th column. The bottom vertices are at the 5th row, end of the 10th column. This positioning suggests a rotation and movement toward the right but similar height to Figure 1.

• Figure 3: The base left vertex is at the bottom of the 6th row, start of the 5th column and the base right vertex at the bottom of the 6th row end of the 7th column. The top vertex position at the 5th row suggests a rotation or reflection.

• Figure 4: This triangle is larger and has its vertices positioned differently, indicating that it may not be a simple rotation/dilation of Figure 1.

• Figure 5: The top vertex is at the top of the 8th row, start of the 3rd column, with the bottom vertex at the 10th row, also in the 3rd column. The right vertex is between the 8th and 9th rows. This positioning indicates a downward stretch.

Given all this information, it appears that Figure 2 is the most likely result of a rotation and dilation of Figure 1, as it maintains a similar height and reflects a rotation about the grid without changing the triangle’s shape significantly.

Thus, the answer is:

Figure 2