https://file.aiquickdraw.com/mathbot/file/1725985344914tn075e8j.jpg

The problem asks to graph the image of parallelogram **ABCD** after a translation of **5 units to the left** and **2 units down**.

### Let's break down the process step-by-step:

1. **Translation Rule**: 
   - For a translation **5 units to the left**: subtract 5 from the **x-coordinate**.
   - For a translation **2 units down**: subtract 2 from the **y-coordinate**.

2. **Current Coordinates** of the parallelogram vertices:
   - \( A = (0, 4) \)
   - \( B = (6, 4) \)
   - \( C = (6, -2) \)
   - \( D = (0, -2) \)

3. **New Coordinates** after translation:
   - \( A' = (0 - 5, 4 - 2) = (-5, 2) \)
   - \( B' = (6 - 5, 4 - 2) = (1, 2) \)
   - \( C' = (6 - 5, -2 - 2) = (1, -4) \)
   - \( D' = (0 - 5, -2 - 2) = (-5, -4) \)

Now that we have the new coordinates of the parallelogram after the translation, you can plot these points to graph the translated parallelogram.

Would you like to ask for further details or any clarification?

Here are 5 related questions:
1. How do you calculate the translation of points in any direction?
2. What other transformations can be applied to a figure besides translation?
3. How can we determine if two shapes are congruent after a transformation?
4. What is the significance of the parallelogram in coordinate geometry?
5. How would a reflection differ from a translation in this case?

**Tip**: Always apply translations to each vertex individually for accuracy when graphing transformations!

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 a parallelogram ABCD by 5 units to the left and 2 units down. This problem covers key concepts in coordinate geometry, including translation rules and applying transformations to polygons. Suitable for students in Grades 7-9.

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