https://file.aiquickdraw.com/mathbot/file/17259848130394c6jb2f9.jpg

The problem asks for a translation of parallelogram ABCD by 5 units to the left and 2 units down. Let's follow the translation step-by-step by modifying the coordinates of each vertex.

### Coordinates of the vertices of parallelogram ABCD:
- **A(0, 4)**
- **B(2, 4)**
- **C(4, 2)**
- **D(2, 2)**

### Translation instructions:
- Move **5 units to the left**: This affects the x-coordinates (subtract 5 from each x-coordinate).
- Move **2 units down**: This affects the y-coordinates (subtract 2 from each y-coordinate).

#### Translated coordinates:
- **A'(0 - 5, 4 - 2) = (-5, 2)**
- **B'(2 - 5, 4 - 2) = (-3, 2)**
- **C'(4 - 5, 2 - 2) = (-1, 0)**
- **D'(2 - 5, 2 - 2) = (-3, 0)**

Now the new parallelogram A'B'C'D' has the following vertices:
- **A'(-5, 2)**
- **B'(-3, 2)**
- **C'(-1, 0)**
- **D'(-3, 0)**

These are the coordinates of the translated parallelogram. If you graph these points, you will see the image of the parallelogram shifted 5 units to the left and 2 units down from its original position.

Let me know if you'd like more details or have any questions!

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Here are 5 related questions to practice:
1. What would happen if the translation was 3 units to the right and 4 units up?
2. How do you determine the center of a parallelogram from its vertices?
3. What is the area of parallelogram ABCD based on its vertices?
4. How would a reflection over the y-axis affect the coordinates of the parallelogram?
5. Can you find the slope of the lines AB and CD?

**Tip:** When translating shapes, pay careful attention to whether you're affecting the x-coordinates or the y-coordinates to avoid mistakes.

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

This page covers how to graph the image of parallelogram ABCD after translating it 5 units to the left and 2 units down. Explore coordinate geometry and the step-by-step process to find the new vertices A', B', C', and D'. Suitable for students in Grades 6-8.

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