To solve this problem, we need to translate each shape on the grid according to the given instructions. A translation means sliding the shape without rotating or flipping it. We'll move each point of the shape by the specified number of units in the x and y directions.
Let’s go through each one:
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1. Translate by (-2, -3)
This means:
- Move every point 2 units to the left (because x decreases by 2)
- Move every point 3 units down (because y decreases by 3)
Original triangle has vertices at approximately:
- A: (-4, -2)
- B: (-2, 2)
- C: (2, 2)
After translation:
- A’ = (-4 - 2, -2 - 3) = (-6, -5)
- B’ = (-2 - 2, 2 - 3) = (-4, -1)
- C’ = (2 - 2, 2 - 3) = (0, -1)
Plot these new points and connect them to form the translated triangle.
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2. Translate by (-1, 3)
This means:
- Move every point 1 unit to the left
- Move every point 3 units up
Original quadrilateral has vertices at approximately:
- A: (-3, 1)
- B: (-1, 2)
- C: (0, 1)
- D: (0, -3)
After translation:
- A’ = (-3 -1, 1 + 3) = (-4, 4)
- B’ = (-1 -1, 2 + 3) = (-2, 5)
- C’ = (0 -1, 1 + 3) = (-1, 4)
- D’ = (0 -1, -3 + 3) = (-1, 0)
Plot these and connect in same order.
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3. Translate by (2, 2)
This means:
- Move every point 2 units right
- Move every point 2 units up
Original triangle has vertices at approximately:
- A: (-4, 0)
- B: (-2, -2)
- C: (-1, 0)
After translation:
- A’ = (-4 + 2, 0 + 2) = (-2, 2)
- B’ = (-2 + 2, -2 + 2) = (0, 0)
- C’ = (-1 + 2, 0 + 2) = (1, 2)
Plot and connect.
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4. Translate by (-3, 2)
This means:
- Move every point 3 units left
- Move every point 2 units up
Original triangle has vertices at approximately:
- A: (-3, -1)
- B: (0, 3)
- C: (3, -2)
After translation:
- A’ = (-3 -3, -1 + 2) = (-6, 1)
- B’ = (0 -3, 3 + 2) = (-3, 5)
- C’ = (3 -3, -2 + 2) = (0, 0)
Plot and connect.
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All translations are done by adding the translation vector to each vertex coordinate. The shape stays the same — only its position changes.
Final Answer:
The translated images are drawn by moving each vertex of the original shapes according to the given translation vectors:
- Top-left: shift 2 left, 3 down
- Top-right: shift 1 left, 3 up
- Bottom-left: shift 2 right, 2 up
- Bottom-right: shift 3 left, 2 up
Each new shape is congruent to the original and positioned accordingly on the grid.
Parent Tip: Review the logic above to help your child master the concept of translations practice worksheet.
