Question
quadrilateral EFGH was dilated and rotated 90 degrees clockwise about the origin to form quadrilateral EFG. which part of quadrilateral EFH is congruent to quadrilateral EFG?
Answers
GPT-4o mini
To analyze the problem, let's first clarify what happens during a dilation and a rotation:
1. **Dilation**: This transformation changes the size of the figure but keeps the shape proportionate. When a figure is dilated, corresponding points in the original and dilated figures maintain the same relative positions.
2. **Rotation**: Specifically, a rotation of 90 degrees clockwise about the origin means that each point (x, y) of the original quadrilateral will be transformed to (y, -x) in the rotated quadrilateral.
Given that quadrilateral EFGH is dilated and then rotated to form quadrilateral EFG, we need to determine which part of quadrilateral EFH is congruent to quadrilateral EFG.
Since EFG is formed from EFGH through these transformations, specifically after the dilation and rotation, the corresponding parts of quadrilateral EFGH that are congruent to quadrilateral EFG will be segments EF and EH, as they maintain their proportions and shapes through the transformations.
Therefore, the corresponding sides and angles of quadrilateral EFH that are congruent to those of EFG would be sides EF and EH.
1. **Dilation**: This transformation changes the size of the figure but keeps the shape proportionate. When a figure is dilated, corresponding points in the original and dilated figures maintain the same relative positions.
2. **Rotation**: Specifically, a rotation of 90 degrees clockwise about the origin means that each point (x, y) of the original quadrilateral will be transformed to (y, -x) in the rotated quadrilateral.
Given that quadrilateral EFGH is dilated and then rotated to form quadrilateral EFG, we need to determine which part of quadrilateral EFH is congruent to quadrilateral EFG.
Since EFG is formed from EFGH through these transformations, specifically after the dilation and rotation, the corresponding parts of quadrilateral EFGH that are congruent to quadrilateral EFG will be segments EF and EH, as they maintain their proportions and shapes through the transformations.
Therefore, the corresponding sides and angles of quadrilateral EFH that are congruent to those of EFG would be sides EF and EH.