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The problem asks to translate the parallelogram \( ABCD \) by 5 units to the left and 2 units down.

### Step-by-step translation process:

- **Translation rule**: 
  - Move each point left by 5 units: subtract 5 from the \( x \)-coordinate.
  - Move each point down by 2 units: subtract 2 from the \( y \)-coordinate.

### Original coordinates of vertices:
From the graph:
- \( A = (2, 4) \)
- \( B = (5, 4) \)
- \( C = (4, 2) \)
- \( D = (1, 2) \)

### Applying the translation to each point:
- \( A' = (2 - 5, 4 - 2) = (-3, 2) \)
- \( B' = (5 - 5, 4 - 2) = (0, 2) \)
- \( C' = (4 - 5, 2 - 2) = (-1, 0) \)
- \( D' = (1 - 5, 2 - 2) = (-4, 0) \)

### New coordinates after translation:
- \( A' = (-3, 2) \)
- \( B' = (0, 2) \)
- \( C' = (-1, 0) \)
- \( D' = (-4, 0) \)

Now, the translated parallelogram \( A'B'C'D' \) can be graphed by plotting these new points.

Would you like more details, or do you have any questions about this process?

Here are 5 questions to further explore this concept:
1. How would a translation by different units (e.g., 3 units right and 1 unit up) affect the parallelogram's vertices?
2. Can you describe the steps to reflect parallelogram \( ABCD \) over the x-axis instead of translating it?
3. What changes to the shape occur when a figure is translated compared to when it is rotated?
4. If you apply two consecutive translations to the parallelogram, how would you determine the overall translation?
5. How could you use a translation matrix to achieve this transformation in a more formal mathematical approach?

**Tip**: When translating a shape, always adjust both the \( x \)- and \( y \)-coordinates by the specified amounts to ensure proper placement in the new position.

The figure shows parallelogram ABCD. Graph the image of the parallelogram after a translation of 5 units to the left and 2 units down.

Learn how to graph the translation of parallelogram ABCD by 5 units left and 2 units down. This problem demonstrates the application of translation rules in coordinate geometry. Suitable for students in Grades 6-8.

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