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To find the translation rule that maps triangle \( \Delta CDE \) to \( \Delta C'D'E' \), we need to observe how the points of the triangle are moved. Specifically, we can compare the coordinates of corresponding points from each triangle.

Let's start with the coordinates of the points:
- \( C(-9, 1) \) and \( C'(1, -7) \)
- \( D(-6, 4) \) and \( D'(4, -4) \)
- \( E(-7, 9) \) and \( E'(3, 2) \)

Now, let's find the horizontal (x-coordinate) and vertical (y-coordinate) shifts between the original points and their corresponding images.

For point \( C \) to \( C' \):
- The x-coordinate changes from -9 to 1, so the change is \( 1 - (-9) = 10 \).
- The y-coordinate changes from 1 to -7, so the change is \( -7 - 1 = -8 \).

Therefore, the translation rule is:
\[
(x, y) \mapsto (x + 10, y - 8)
\]

This rule indicates that every point in \( \Delta CDE \) is shifted 10 units to the right and 8 units down to obtain \( \Delta C'D'E' \).

Would you like further details or have any questions about this? 

Here are 5 related questions you might find interesting:
1. How would the translation rule change if the triangles were reflected instead of translated?
2. How can you determine if two shapes are congruent using translation rules?
3. Can a translation rule ever have negative values for both x and y shifts? What would that look like?
4. How does the translation rule relate to vector mathematics?
5. How could you apply this translation rule to a non-triangular shape, like a square or rectangle?

**Tip:** When determining translations on a coordinate plane, always start by comparing corresponding points to find consistent horizontal and vertical shifts.

ΔC'D'E' is a translation of ΔCDE. Write the translation rule.

Learn how to find the translation rule for mapping triangle ΔCDE to ΔC'D'E' in coordinate geometry. This problem covers translation concepts, and the solution involves comparing corresponding points to find horizontal and vertical shifts. Suitable for students in Grades 6-8.

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