https://file.aiquickdraw.com/mathbot/file/1725984804336zi7zce4z.jpg

To solve this problem, we need to perform a translation on the given parallelogram \( ABCD \) by shifting each vertex 5 units to the left and 2 units down. Let's go step-by-step.

### Given Coordinates of Parallelogram \( ABCD \):
- \( A (0, 4) \)
- \( B (4, 4) \)
- \( C (6, 0) \)
- \( D (2, 0) \)

### Translation Rule:
- Left 5 units means subtract 5 from the x-coordinate.
- Down 2 units means subtract 2 from the y-coordinate.

### New Coordinates after Translation:
1. **Point \( A (0, 4) \)**:
   - \( x' = 0 - 5 = -5 \)
   - \( y' = 4 - 2 = 2 \)
   - New \( A' = (-5, 2) \)

2. **Point \( B (4, 4) \)**:
   - \( x' = 4 - 5 = -1 \)
   - \( y' = 4 - 2 = 2 \)
   - New \( B' = (-1, 2) \)

3. **Point \( C (6, 0) \)**:
   - \( x' = 6 - 5 = 1 \)
   - \( y' = 0 - 2 = -2 \)
   - New \( C' = (1, -2) \)

4. **Point \( D (2, 0) \)**:
   - \( x' = 2 - 5 = -3 \)
   - \( y' = 0 - 2 = -2 \)
   - New \( D' = (-3, -2) \)

### Summary:
- \( A' = (-5, 2) \)
- \( B' = (-1, 2) \)
- \( C' = (1, -2) \)
- \( D' = (-3, -2) \)

You can now graph the parallelogram using these new coordinates to show the image after the translation.

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Would you like any additional details or further explanation?

Here are 5 questions to consider:
1. What is the geometric interpretation of translating shapes?
2. How can you check if the translation was applied correctly?
3. How would the translation affect a general polygon, like a triangle?
4. Can you perform translations using matrix transformations?
5. What happens if we translate a shape by both positive and negative values?

**Tip**: Always apply translation rules consistently to each vertex of the shape to avoid errors.

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 translate parallelogram ABCD on the coordinate plane by 5 units to the left and 2 units down. This problem focuses on geometric transformations, particularly translations, and is suitable for students in Grades 6-8.

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