https://file.aiquickdraw.com/mathbot/file/1726577712491a0h5oz9x.jpg

The problem in the image is asking to **translate** the given figure (the pink polygon) **3 units left** and **6 units down** on a coordinate plane. The resulting figure after the translation (the blue polygon) is shown on the graph.

### Steps to translate the figure:
1. **Translation rule**:
   - Move each point of the figure 3 units to the left: This means subtracting 3 from the x-coordinate of each point.
   - Move each point 6 units down: This means subtracting 6 from the y-coordinate of each point.

2. **Verify the coordinates**:
   - Start with the original points of the pink figure (which are not labeled in the image but can be approximated based on the grid).
   - Apply the translation to each point and plot the new points.

3. **Check alignment**:
   - The blue figure appears to be the correct translation of the pink figure, where each vertex is moved 3 units left and 6 units down.

Would you like more details on the specific translation process, or any clarifications on the steps?

### Related Questions:
1. How do you determine the coordinates of a point after a translation?
2. Can translation ever change the size or shape of a figure?
3. How would you describe a reflection compared to a translation on the coordinate plane?
4. What is the effect of translating a point only along the x-axis or y-axis?
5. How does translation relate to other types of transformations (like rotations or dilations)?

#### Tip:
When performing translations on a coordinate plane, always remember that translations preserve the shape, size, and orientation of the figure; they only shift the position.

Translate the figure 3 units left and 6 units down.

Learn how to translate a figure on the coordinate plane 3 units left and 6 units down. This problem covers key concepts of geometry, including coordinate translation and the preservation of shape and size. Suitable for students in Grades 6-8.

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