https://file.aiquickdraw.com/mathbot/file/172848731976423phifmm.jpg

To translate the triangle in the image 3 units to the right and 2 units down, you need to apply the following translation to each vertex of the triangle:

- Add 3 to the x-coordinate (right shift).
- Subtract 2 from the y-coordinate (down shift).

### Let's go step-by-step:

1. Identify the coordinates of the triangle's vertices from the graph. For the sake of example, let's estimate the vertices as follows (you may need to adjust based on exact coordinates):
   - Vertex A: (-4, 5)
   - Vertex B: (-6, -1)
   - Vertex C: (0, -2)

2. Apply the translation (3 units to the right and 2 units down) to each vertex:
   - New Vertex A: (-4 + 3, 5 - 2) = (-1, 3)
   - New Vertex B: (-6 + 3, -1 - 2) = (-3, -3)
   - New Vertex C: (0 + 3, -2 - 2) = (3, -4)

3. Plot these new coordinates on the graph to draw the translated triangle.

This will give you the image of the triangle after the transformation.

Would you like any further details or clarification on this process?

Here are 5 related questions to deepen your understanding:
1. How does the translation affect the shape and orientation of the triangle?
2. What are the differences between translation, rotation, and reflection in geometry?
3. If the triangle were translated 5 units left and 3 units up, what would the new coordinates be?
4. How would you describe the translation algebraically in terms of vector notation?
5. What is the effect of multiple translations applied successively on a shape?

**Tip:** When translating shapes, remember that translations only affect position, not the size or orientation of the shape.

Draw the following triangle after a translation 3 units to the right and 2 units down.

Learn how to translate a triangle 3 units to the right and 2 units down using coordinate geometry. This step-by-step guide explains how to modify the coordinates of each vertex to apply the transformation. Suitable for Grades 6-8.

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