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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 3
Figure 3

Figure 2
Figure 2

Figure 5
Figure 5

Figure 4
Figure 4
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Answer 1

To determine which figure would result from rotating and dilating Figure 1, let’s first analyze the positioning and dimensions of Figure 1 in comparison to the other figures.

• Figure 1:
  • Top vertex at (3, 3) (row, column)
  • Bottom vertex at (5, 3)
  • Right vertex at approximately (4, 4)

Looking at the positions of the other figures:

• Figure 2:

  • Top vertex at (3, 10)
  • Bottom vertex at (5, 10)
  • Left vertex at approximately (4, 9)

• Figure 3:

  • Top vertex at (5, 6) (slightly shifted to the right)
  • Base vertices at (6, 5) and (6, 7)

• Figure 4:

  • Larger triangle with a different orientation altogether.

• Figure 5:

  • Top vertex at (8, 3)
  • Bottom vertex at (10, 3)
  • Right vertex at (9, 4)

Now let's analyze potential rotations for Figure 1. If Figure 1 is rotated, it could potentially yield a figure positioned differently but retaining the triangular shape.

Upon analyzing, if we visualize the results after rotating Figure 1 90 degrees clockwise, we might get a triangle closer in orientation to that of Figure 2.

After dilation, the dimensions would slightly grow, but the relative positions of vertices from the original will still align closely with those of Figure 2.

Thus, the answer is: Figure 2