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.

Question

Which figure would result from rotating and dilating Figure 1?

Figure 5

Figure 2

Figure 4

Figure 3

Answer 1

To determine which figure would result from rotating and dilating Figure 1, we need to analyze the geometric transformations involved.

Figure 1 has:

• A top vertex located at (3rd row, 3rd column)
• A bottom vertex at (5th row, 3rd column)
• A right vertex at (between 3rd and 4th rows, 4th column)

Figure 5 has:

• A top vertex at (8th row, 3rd column)
• A bottom vertex at (10th row, 3rd column)
• A right vertex at (between 8th and 9th rows, 4th column)

Observing the relative positioning:

• The left-to-right alignment remains the same in both figures.
• Figure 5 is located further down the grid compared to Figure 1.

To rotate Figure 1, the orientation of the triangle changes, and it needs to be compared with other figures to see if it matches with any through rotation and dilation.

Figures 2, 3, and 4 can similarly be analyzed for alignment of their vertices and respective placements within the grid. However, only Figure 5 retains the corresponding left-to-right edge orientation and the overall triangular shape after adjusting for size changes.

By interpreting dilation (scaling the triangle size) and the rotation needed to align with Figure 5, we conclude that Figure 5 is likely the product of rotating and dilating Figure 1.

Thus, the answer is: Figure 5.