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The problem asks for the translation that maps quadrilateral \( ABCD \) (blue points) to quadrilateral \( A'B'C'D' \) (magenta points). To find the translation, we can compare the coordinates of corresponding points on each quadrilateral. 

Let’s find the translation by looking at the point \( A \) and its corresponding point \( A' \):

- Point \( A \) is located at \( (-6, -1) \).
- Point \( A' \) is located at \( (-3, 3) \).

To determine the translation:

1. **Horizontal movement** (x-axis): From \( -6 \) to \( -3 \), there is a translation of \( +3 \) units to the right.
2. **Vertical movement** (y-axis): From \( -1 \) to \( 3 \), there is a translation of \( +4 \) units up.

Thus, the translation is **3 units to the right** and **4 units up**.

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

Here are 5 related questions to expand on this concept:
1. How do you find the translation of a different point, such as \( B \) to \( B' \)?
2. What is the rule of translation that applies to all points in this scenario?
3. Can you perform the reverse translation from \( A'B'C'D' \) back to \( ABCD \)?
4. What other transformations, like rotations or reflections, could map one quadrilateral to the other?
5. How does the concept of translation relate to vectors in coordinate geometry?

**Tip:** To verify your translation, you can apply the translation rule to every vertex and check if they match their corresponding translated points.

Determine the translation that maps quadrilateral ABCD (blue points) to quadrilateral A'B'C'D' (magenta points).

Learn how to determine the translation of quadrilateral ABCD to A'B'C'D' using coordinate geometry. This step-by-step solution demonstrates how to calculate the horizontal and vertical shifts for each point. Suitable for students in Grades 8-10.

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