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The problem involves translating the triangle \( ABC \) by 3 units to the left and 5 units down. The given image shows the triangle's current coordinates on a grid:

- \( A(5, 5) \)
- \( B(2, 1) \)
- \( C(7, 3) \)

To apply the translation:
- Subtract 3 from the \( x \)-coordinates (move 3 units left).
- Subtract 5 from the \( y \)-coordinates (move 5 units down).

Let's compute the new coordinates for each vertex:
1. For point \( A(5, 5) \):
   \[
   A' = (5 - 3, 5 - 5) = (2, 0)
   \]
2. For point \( B(2, 1) \):
   \[
   B' = (2 - 3, 1 - 5) = (-1, -4)
   \]
3. For point \( C(7, 3) \):
   \[
   C' = (7 - 3, 3 - 5) = (4, -2)
   \]

Thus, the coordinates of the new triangle \( A'B'C' \) are:
- \( A'(2, 0) \)
- \( B'(-1, -4) \)
- \( C'(4, -2) \)

Among the provided options, the correct coordinates are not directly listed. However, the transformation process is correct, so if you need to recheck the problem setup, feel free to ask!

Would you like further explanation on the steps or have more questions?

Here are 5 related questions:
1. How do translations differ from rotations?
2. How would the coordinates change if the translation was 4 units right and 2 units up?
3. What is the general formula for translating a point \( (x, y) \)?
4. How can translations be represented in matrix form?
5. How would this problem change if the triangle were reflected instead?

**Tip:** Always double-check the original points' coordinates before applying transformations to ensure accuracy.

Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of the new triangle A'B'C'?

Explore the translation of triangle ABC by moving it 3 units left and 5 units down. Learn how to apply geometric translations to find the new coordinates of the triangle vertices A', B', and C'. This problem is perfect for students in Grades 6-8 studying coordinate geometry and translations.

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