Math Problem Statement

Describe a sequence of transformations that takes ABCD to A'B'C'D'.

Solution

To describe the sequence of transformations that takes ABCDABCD to ABCDA'B'C'D', let's analyze the two shapes.

  • ABCDABCD is located on the left-hand side of the yy-axis, while ABCDA'B'C'D' is located on the right-hand side.
  • The shapes are reflected versions of each other, suggesting either a reflection or a rotation, followed by translation.

Steps:

  1. Reflection over the yy-axis: This would place ABCDABCD on the right side of the graph where ABCDA'B'C'D' is located.
  2. Translation down: Once reflected, the shape needs to move down by 1 unit to align perfectly with ABCDA'B'C'D'.

Thus, the correct sequence is:

  • B: Reflect ABCDABCD over the yy-axis, then translate down 1.

Do you want any further clarification on this?

Related Questions:

  1. What happens if you reflect a shape over the xx-axis instead of the yy-axis?
  2. How can you identify if a transformation includes rotation instead of reflection?
  3. How would you describe a 180-degree rotation transformation around a point?
  4. What would happen if you translated a shape up instead of down?
  5. How can you distinguish between clockwise and counterclockwise rotations?

Tip:

Always check the orientation of the shape before and after transformation to identify whether a reflection or rotation occurred.

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Math Problem Analysis

Mathematical Concepts

Geometric Transformations
Reflections
Translations
Rotations

Formulas

Reflection over x-axis or y-axis formulas
Translation formula: (x, y) -> (x, y ± n)

Theorems

Transformational Geometry Theorems

Suitable Grade Level

Grades 8-9