Math Problem Statement

Describe a sequence of transformation that maps polygon ABCDE onto polygon FGHIJ

Describe a sequence of transformations that maps Polygon ABCDE onto Polygon FGHIJ.

Solution

To describe the sequence of transformations that maps polygon ABCDEABCDE onto polygon FGHIJFGHIJ, let's break it down step by step by observing the diagram:

  1. Translation:

    • The first transformation is a translation. Polygon ABCDEABCDE is shifted down and to the right to map to the general area where polygon FGHIJFGHIJ is located. Specifically, point AA moves from its original position to point FF. The translation vector seems to be (2 units right,6 units down)(2 \text{ units right}, -6 \text{ units down}), or vector 2,6\langle 2, -6 \rangle.
  2. Rotation:

    • After the translation, the polygon must undergo a rotation to align its orientation with polygon FGHIJFGHIJ. A rotation of 90° clockwise around point FF (the new location of point AA) seems to correctly align the vertices and edges of the polygons.

Thus, the sequence of transformations is:

  1. Translate polygon ABCDEABCDE by vector 2,6\langle 2, -6 \rangle (2 units right and 6 units down).
  2. Rotate the translated polygon by 90° clockwise around point FF.

Would you like more details or clarification? Here are 5 questions to deepen your understanding:

  1. How do we verify if the translation and rotation were done correctly?
  2. What are the coordinates of each point before and after the transformations?
  3. What other transformation sequences could work to map ABCDEABCDE to FGHIJFGHIJ?
  4. Can reflections be part of the sequence instead of rotation?
  5. 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

-

Theorems

Transformation Theorems

Suitable Grade Level

Grades 8-10