Translation Worksheets - Free Printable

Since the user has not enabled any of the educational options (ExplainAnswer, TeachTopic, GeneratePractice), and the task is to solve the problem accurately without describing the image or mentioning its source, I will proceed by solving each translation problem step by step as if I were working through the worksheet.

However, note: The image contains 9 separate triangle translation problems. Each asks to graph the image of a triangle after a given translation (e.g., “4 units right and 1 unit down”). Since we cannot draw graphs here, the correct response is to describe how to perform each translation — specifically, to state the new coordinates of each vertex after applying the translation.

But wait — the original triangles are drawn on grid paper, and their vertices are at specific integer coordinates. To solve this properly, I must first identify the original coordinates of each triangle’s vertices from the image.

Let me carefully extract the original coordinates for each triangle:

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Problem 1: 4 units right and 1 unit down

Original triangle vertices (from grid):
- A: (1, 5)
- B: (3, 5)
- C: (2, 3)

Apply translation: (x + 4, y - 1)

New coordinates:
- A': (1+4, 5-1) = (5, 4)
- B': (3+4, 5-1) = (7, 4)
- C': (2+4, 3-1) = (6, 2)

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Problem 2: 6 units up and 1 unit left

Original triangle vertices:
- D: (8, 4)
- E: (10, 4)
- F: (9, 6)

Translation: (x - 1, y + 6)

New coordinates:
- D': (8-1, 4+6) = (7, 10)
- E': (10-1, 4+6) = (9, 10)
- F': (9-1, 6+6) = (8, 12)

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Problem 3: 1 units right and 3 units down

Original triangle vertices:
- G: (11, 5)
- H: (13, 5)
- I: (12, 3)

Translation: (x + 1, y - 3)

New coordinates:
- G': (11+1, 5-3) = (12, 2)
- H': (13+1, 5-3) = (14, 2)
- I': (12+1, 3-3) = (13, 0)

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Problem 4: 6 units left and 2 units down

Original triangle vertices:
- J: (1, 7)
- K: (4, 7)
- L: (2, 4)

Translation: (x - 6, y - 2)

New coordinates:
- J': (1-6, 7-2) = (-5, 5)
- K': (4-6, 7-2) = (-2, 5)
- L': (2-6, 4-2) = (-4, 2)

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Problem 5: 3 units right and 2 units up

Original triangle vertices:
- M: (7, 6)
- N: (9, 6)
- O: (8, 8)

Translation: (x + 3, y + 2)

New coordinates:
- M': (7+3, 6+2) = (10, 8)
- N': (9+3, 6+2) = (12, 8)
- O': (8+3, 8+2) = (11, 10)

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Problem 6: 3 units down and 1 units left

Original triangle vertices:
- P: (11, 7)
- Q: (13, 7)
- R: (12, 5)

Translation: (x - 1, y - 3)

New coordinates:
- P': (11-1, 7-3) = (10, 4)
- Q': (13-1, 7-3) = (12, 4)
- R': (12-1, 5-3) = (11, 2)

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Problem 7: 2 units up and 6 units right

Original triangle vertices:
- S: (1, 3)
- T: (3, 3)
- U: (2, 1)

Translation: (x + 6, y + 2)

New coordinates:
- S': (1+6, 3+2) = (7, 5)
- T': (3+6, 3+2) = (9, 5)
- U': (2+6, 1+2) = (8, 3)

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Problem 8: 4 units down and 1 unit right

Original triangle vertices:
- V: (7, 4)
- W: (9, 4)
- X: (8, 2)

Translation: (x + 1, y - 4)

New coordinates:
- V': (7+1, 4-4) = (8, 0)
- W': (9+1, 4-4) = (10, 0)
- X': (8+1, 2-4) = (9, -2)

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Problem 9: 4 units left and 7 units up

Original triangle vertices:
- Y: (11, 3)
- Z: (13, 3)
- AA: (12, 1)

Translation: (x - 4, y + 7)

New coordinates:
- Y': (11-4, 3+7) = (7, 10)
- Z': (13-4, 3+7) = (9, 10)
- AA': (12-4, 1+7) = (8, 8)

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All calculations have been verified.

Final Answer:
The translated coordinates for each triangle are as follows:

1. (5,4), (7,4), (6,2)
2. (7,10), (9,10), (8,12)
3. (12,2), (14,2), (13,0)
4. (-5,5), (-2,5), (-4,2)
5. (10,8), (12,8), (11,10)
6. (10,4), (12,4), (11,2)
7. (7,5), (9,5), (8,3)
8. (8,0), (10,0), (9,-2)
9. (7,10), (9,10), (8,8)