Similar Figures Practice

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An illustration shows four trapezoids labeled Figure 1, Figure 2, Figure 3 and Figure 4 that are placed on a 17 column by 15 row grid. Figures 1 and 2 are the same size, while Figure 3 is smaller than the others and Figure 4 is larger than the others. Figure 1 shows the top left vertex on top of the 3rd row and the end of the 3rd column, the top right vertex on top of the 3rd row and the start of the 6th column, the bottom left vertex on the bottom of the 4th row and the start of the 3rd column, and the bottom right vertex on the bottom of the 4th row and the end of the 6th column. Figure 2 shows the top left vertex on top of the 3rd row and the end of the 11th column, the top right vertex on top of the 3rd row and the start of the 14th column, the bottom left vertex on the bottom of the 4th row and the start of 11th column, and the bottom right vertex on the bottom of the 4th row and the end of the 14th column. Figure 3 shows the top left vertex on top of the 7th row and the middle of the 4th column, the top right vertex on the top of the 7th row and the start of the 5th column, the bottom left vertex on the bottom of 7th row and the start of the 4th column, and the bottom right vertex on the bottom of the 7th row and end of 5th column. Figure 4 is inclined at an angle. It shows the top left vertex on top of the 8th row and the middle of the 12th column, the top right vertex on the bottom of 9th row and the end of the 15th column, the bottom left vertex on the middle of the 10th row and start of 9th column, and bottom right vertex on the 14th row and 15th column.

Which figure would result from rotating and dilating Figure 1?

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Answer 1

To determine which figure would result from rotating and dilating Figure 1, we need to consider the properties involved in these transformations.

1. Rotation: This involves turning the figure around a point (usually the origin, but can be any point). The angles of rotation could be 90 degrees, 180 degrees, etc.

2. Dilation: This involves resizing the figure, which can make it larger (enlargement) or smaller (reduction) while keeping the same proportions and angles.

Based on your description:

• Figure 1 has specific coordinates and dimensions.
• Figure 2 is the same size as Figure 1 but is positioned differently on the grid.
• Figure 3 is smaller than the others, suggesting it has undergone a dilation (reduction).
• Figure 4 is larger than the others and also inclined, indicating it has likely undergone an enlargement and perhaps a rotation.

If we assume a standard rotation without any drastic changes in position besides what’s allowed by rotation (like moving its location within the grid) and consistent proportions due to dilation, Figure 2 seems like a likely result because it retains the same size as Figure 1 but is oriented differently.

Thus, if you rotate and dilate Figure 1:

• From reference, the best answer would be Figure 2, assuming it underwent no change in size (only different positioning), making it the most appropriate choice for this scenario unless additional specific rotation and dilation are applied on Figure 1 to look exactly like Figure 2.

So, select Figure 2 as your answer.