Math Problem Statement
Describe a sequence of transformation that maps polygon ABCDE onto polygon FGHIJ
Solution
To describe the sequence of transformations that maps polygon onto polygon , let's break it down step by step by observing the diagram:
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Translation:
- The first transformation is a translation. Polygon is shifted down and to the right to map to the general area where polygon is located. Specifically, point moves from its original position to point . The translation vector seems to be , or vector .
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Rotation:
- After the translation, the polygon must undergo a rotation to align its orientation with polygon . A rotation of 90° clockwise around point (the new location of point ) seems to correctly align the vertices and edges of the polygons.
Thus, the sequence of transformations is:
- Translate polygon by vector (2 units right and 6 units down).
- Rotate the translated polygon by 90° clockwise around point .
Would you like more details or clarification? Here are 5 questions to deepen your understanding:
- How do we verify if the translation and rotation were done correctly?
- What are the coordinates of each point before and after the transformations?
- What other transformation sequences could work to map to ?
- Can reflections be part of the sequence instead of rotation?
- How does the transformation affect the orientation of the polygon?
Tip: When applying transformations, always check the new positions of corresponding points to confirm alignment.
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Math Problem Analysis
Mathematical Concepts
Geometric Transformations
Translations
Rotations
Formulas
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Theorems
Transformation Theorems
Suitable Grade Level
Grades 8-10
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