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To find the translation rule for \( \triangle TUV \) to \( \triangle T'U'V' \), we need to determine how each vertex of \( \triangle TUV \) has been moved to its corresponding point in \( \triangle T'U'V' \).

Let's look at the coordinates of the vertices:

- \( T \) is located at \( (-8, 0) \) and \( T' \) is located at \( (2, -10) \).
- \( U \) is located at \( (-4, 8) \) and \( U' \) is located at \( (6, -2) \).
- \( V \) is located at \( (0, 0) \) and \( V' \) is located at \( (10, -10) \).

Now, we calculate the translation for each point:

1. From \( T(-8, 0) \) to \( T'(2, -10) \), the translation is:
   \[
   \Delta x = 2 - (-8) = 10, \quad \Delta y = -10 - 0 = -10
   \]
   
2. From \( U(-4, 8) \) to \( U'(6, -2) \), the translation is:
   \[
   \Delta x = 6 - (-4) = 10, \quad \Delta y = -2 - 8 = -10
   \]
   
3. From \( V(0, 0) \) to \( V'(10, -10) \), the translation is:
   \[
   \Delta x = 10 - 0 = 10, \quad \Delta y = -10 - 0 = -10
   \]

Since the translation is consistent for all vertices, the rule for translation is:

\[
(x, y) \mapsto (x + 10, y - 10)
\]

Would you like more details or have any questions? 

Here are 5 related questions to explore:

1. How do you verify that a transformation is a translation?
2. What are other types of transformations besides translation?
3. How can you describe the movement of shapes on the coordinate plane using vectors?
4. How would you calculate the distance between two corresponding points after translation?
5. What is the significance of maintaining shape congruence in translations?

**Tip:** When solving translations, ensure the same change in coordinates applies to all vertices of the shape.

ΔT'U'V' is a translation of ΔTUV. Write the translation rule.

Learn how to determine the translation rule for the triangle ΔTUV to ΔT'U'V'. This problem involves coordinate geometry and translations, suitable for students in Grades 6-8. Follow the step-by-step solution to understand the translation formula and apply it correctly.

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