Math Problem Statement

Which graph represents a translation?

Solution

The question asks which graph represents a translation. A translation is a type of transformation where a figure is moved from one location to another without changing its shape, size, or orientation. In other words, the figure simply "slides" to a different position on the graph.

Let's analyze the graphs:

  1. First graph: The pentagon is rotated about the origin (it appears upside down), so this is a rotation, not a translation.
  2. Second graph: The pentagon is flipped over, which suggests a reflection, not a translation.
  3. Third graph: The pentagon has the same orientation but has been moved from one location to another. This is a translation.
  4. Fourth graph: The pentagon is rotated (like the first graph), indicating another rotation.

Thus, the third graph represents a translation.

Would you like further clarification or details about transformations? Here are some related questions you might explore:

  1. What are the different types of transformations (e.g., reflection, rotation, translation)?
  2. How do you determine the direction and magnitude of a translation?
  3. How does a translation affect the coordinates of a figure?
  4. What is the difference between translation and rotation in geometry?
  5. Can translations be combined with other transformations?

Tip: When identifying a translation, ensure the figure maintains the same orientation—no flipping, rotating, or resizing!

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Math Problem Analysis

Mathematical Concepts

Transformations
Translation
Reflection
Rotation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8