Since the user has not requested explanations, topic teaching, or practice generation (all set to false), I will proceed directly to solving each translation problem step by step and provide the final answers for all six problems.
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Problem 1: Translation — 3 right
Original shape is a triangle in the third quadrant. Let’s pick key points:
- Bottom-left vertex: (-4, -5)
- Top vertex: (-4, -1)
- Right vertex: (-2, -5)
Translate 3 units right → add 3 to x-coordinates:
- (-4 + 3, -5) = (-1, -5)
- (-4 + 3, -1) = (-1, -1)
- (-2 + 3, -5) = (1, -5)
New triangle vertices: (-1, -5), (-1, -1), (1, -5)
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Problem 2: Translation — 2 right and 3 down
Shape is a trapezoid in second quadrant. Key points:
- Top-left: (-5, 4)
- Top-right: (-3, 4)
- Bottom-right: (-3, 2)
- Bottom-left: (-4, 2)
Apply translation: x + 2, y - 3
- (-5+2, 4-3) = (-3, 1)
- (-3+2, 4-3) = (-1, 1)
- (-3+2, 2-3) = (-1, -1)
- (-4+2, 2-3) = (-2, -1)
New vertices: (-3, 1), (-1, 1), (-1, -1), (-2, -1)
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Problem 3: Translation — 5 left
Triangle in fourth quadrant. Points:
- Leftmost: (1, -3)
- Rightmost top: (5, -1)
- Rightmost bottom: (5, -5)
Translate 5 left → subtract 5 from x:
- (1-5, -3) = (-4, -3)
- (5-5, -1) = (0, -1)
- (5-5, -5) = (0, -5)
New vertices: (-4, -3), (0, -1), (0, -5)
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Problem 4: Translation — 4 left and 3 down
L-shaped figure in first quadrant. Points:
- Top-left: (2, 6)
- Top-right: (4, 6)
- Middle-right: (4, 4)
- Bottom-right: (4, 2)
- Bottom-left: (2, 2)
- Inner corner: (2, 4)
Apply: x - 4, y - 3
- (2-4, 6-3) = (-2, 3)
- (4-4, 6-3) = (0, 3)
- (4-4, 4-3) = (0, 1)
- (4-4, 2-3) = (0, -1)
- (2-4, 2-3) = (-2, -1)
- (2-4, 4-3) = (-2, 1)
New vertices: (-2, 3), (0, 3), (0, 1), (0, -1), (-2, -1), (-2, 1)
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Problem 5: Translation — 4 left and 5 down
Quadrilateral in first quadrant. Points:
- Bottom-left: (1, 1)
- Top-left: (1, 4)
- Top-right: (3, 4)
- Bottom-right: (3, 2)
Apply: x - 4, y - 5
- (1-4, 1-5) = (-3, -4)
- (1-4, 4-5) = (-3, -1)
- (3-4, 4-5) = (-1, -1)
- (3-4, 2-5) = (-1, -3)
New vertices: (-3, -4), (-3, -1), (-1, -1), (-1, -3)
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Problem 6: Translation — 3 right and 4 up
Triangle in third quadrant. Points:
- Leftmost: (-4, -4)
- Bottom: (-2, -5)
- Top: (-1, -2)
Apply: x + 3, y + 4
- (-4+3, -4+4) = (-1, 0)
- (-2+3, -5+4) = (1, -1)
- (-1+3, -2+4) = (2, 2)
New vertices: (-1, 0), (1, -1), (2, 2)
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Final Answer:
1) Triangle with vertices at (-1, -5), (-1, -1), (1, -5)
2) Trapezoid with vertices at (-3, 1), (-1, 1), (-1, -1), (-2, -1)
3) Triangle with vertices at (-4, -3), (0, -1), (0, -5)
4) L-shape with vertices at (-2, 3), (0, 3), (0, 1), (0, -1), (-2, -1), (-2, 1)
5) Quadrilateral with vertices at (-3, -4), (-3, -1), (-1, -1), (-1, -3)
6) Triangle with vertices at (-1, 0), (1, -1), (2, 2)
Parent Tip: Review the logic above to help your child master the concept of transformation translation worksheet.
