Math Problem Statement

Which sequence of transformations maps figure 1 onto figure 2?

Solution

To determine the correct sequence of transformations that maps figure 1 onto figure 2, let's examine the position and orientation of each figure.

  1. Step 1: Translation

    • Observing the two figures, we see that figure 1 needs to move to the right and down to reach the position of figure 2. Counting units:
      • From figure 1’s initial position to align with figure 2, it needs a translation of 6 units to the right and 5 units down.
  2. Step 2: Reflection (if needed)

    • After the translation, figure 1 still does not match the orientation of figure 2. Figure 2 appears to be a mirror image of figure 1 across the x-axis, indicating that a reflection across the x-axis is necessary to match the orientation exactly.

Conclusion: The correct sequence of transformations is:

  • A translation of 6 units right and 5 units down, followed by a reflection across the x-axis.

Therefore, the answer is: a translation of 6 units right and 5 units down\boxed{\text{a translation of 6 units right and 5 units down}}

Would you like further clarification on how to identify transformations from coordinates?

Here are 5 related questions:

  1. How do you determine if a figure has been reflected or rotated?
  2. What is the difference between a translation and a reflection in transformations?
  3. How can you determine the axis of reflection for any figure?
  4. What sequence of transformations preserves the orientation of a figure?
  5. How do you perform a translation on a coordinate grid?

Tip: Always apply transformations step-by-step to verify that each aligns with the intended final position and orientation!

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Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Translations
Reflections

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9