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To find the translation rule for parallelogram \( T'U'V'W' \) as a translation of parallelogram \( TUVW \), we need to determine how each vertex of \( TUVW \) is shifted to match the corresponding vertex in \( T'U'V'W' \).

1. **Select corresponding points:**
   - Point \( T \) corresponds to point \( T' \).
   - Point \( U \) corresponds to point \( U' \).
   - Point \( V \) corresponds to point \( V' \).
   - Point \( W \) corresponds to point \( W' \).

2. **Identify coordinates:**
   - From the graph, the coordinates are approximately:
     - \( T(-6, 4) \) and \( T'(2, 0) \),
     - \( U(-4, 8) \) and \( U'(4, 4) \),
     - \( V(2, 8) \) and \( V'(10, 4) \),
     - \( W(0, 4) \) and \( W'(8, 0) \).

3. **Calculate translation:**
   The translation vector \( (a, b) \) can be found by subtracting the coordinates of each original point from its corresponding translated point. For example, using \( T(-6, 4) \) and \( T'(2, 0) \):
   \[
   a = 2 - (-6) = 8
   \]
   \[
   b = 0 - 4 = -4
   \]
   Therefore, the translation rule is:
   \[
   (x, y) \mapsto (x + 8, y - 4)
   \]

Would you like more details on this solution or have any further questions?

Here are 5 related questions for further practice:
1. How would the translation rule change if the parallelogram were shifted left instead of right?
2. What is the relationship between the area of \( TUVW \) and \( T'U'V'W' \)?
3. How would you describe the transformation if the parallelogram were reflected instead of translated?
4. Can you find the translation rule by using any two corresponding points?
5. What other types of transformations (e.g., rotations, dilations) could preserve the shape of the parallelogram?

**Tip:** When performing translations, keep in mind that the shape and size of the figure remain unchanged, only the position shifts.

Parallelogram T'U'V'W' is a translation of parallelogram TUVW. Write the translation rule.

Learn how to find the translation rule of a parallelogram in coordinate geometry. This problem involves shifting parallelogram TUVW to T'U'V'W' and covers key concepts like translation and coordinate shifts. Suitable for students in Grades 6-8.

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