https://file.aiquickdraw.com/mathbot/file/17259847690416owfey4e.jpg

The problem in the image asks to translate parallelogram \( ABCD \) by 5 units to the left and 2 units down. Let's begin by identifying the current coordinates of points \( A \), \( B \), \( C \), and \( D \), and then apply the transformation.

### Current Coordinates:
From the graph:
- \( A(0, 4) \)
- \( B(4, 4) \)
- \( C(5, 2) \)
- \( D(1, 2) \)

### Translation:
A translation of 5 units to the left and 2 units down means we subtract 5 from the x-coordinates and subtract 2 from the y-coordinates of each point. Let's compute the new coordinates:

- \( A'(0 - 5, 4 - 2) = (-5, 2) \)
- \( B'(4 - 5, 4 - 2) = (-1, 2) \)
- \( C'(5 - 5, 2 - 2) = (0, 0) \)
- \( D'(1 - 5, 2 - 2) = (-4, 0) \)

### New Coordinates:
The translated parallelogram will have vertices at:
- \( A'(-5, 2) \)
- \( B'(-1, 2) \)
- \( C'(0, 0) \)
- \( D'(-4, 0) \)

You can now graph these points on the coordinate plane to draw the new image of parallelogram \( ABCD \) after the translation.

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Would you like a detailed explanation of how translations work or have any other questions?

Here are five related questions:
1. What is the general rule for translating a shape in the coordinate plane?
2. How do you perform a reflection instead of a translation?
3. What would happen if we translated the parallelogram 5 units to the right instead?
4. Can you describe the effect of translating a shape upwards or downwards?
5. How does a translation differ from a rotation?

**Tip:** When translating points, always apply the same shift to all vertices to maintain the shape's properties and dimensions.

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 a coordinate plane by 5 units to the left and 2 units down. This problem focuses on geometric translations and graphing. Suitable for students in Grades 6-8.

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