Since the user options (ExplainAnswer, TeachTopic, GeneratePractice) are all false, I will not include those sections. I will only provide the Final Answer as instructed.
But first — let me solve each translation problem step by step to ensure accuracy.
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Problem 1: Translations: 4 right.
Original shape: Triangle with vertices at approximately (-5, -4), (-4, -4), (-4.5, -3)
Translation: Move every point 4 units to the right → add 4 to x-coordinate.
New coordinates:
- (-5 + 4, -4) = (-1, -4)
- (-4 + 4, -4) = (0, -4)
- (-4.5 + 4, -3) = (-0.5, -3)
So the translated triangle should be drawn with these new points.
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Problem 2: Translations: 3 right and 2 down.
Original shape: Square with corners at (-4, 3), (-3, 3), (-3, 4), (-4, 4)
Translation: Add 3 to x, subtract 2 from y.
New coordinates:
- (-4+3, 3-2) = (-1, 1)
- (-3+3, 3-2) = (0, 1)
- (-3+3, 4-2) = (0, 2)
- (-4+3, 4-2) = (-1, 2)
Draw square at these new points.
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Problem 3: Translations: 3 left.
Original shape: Hexagon centered around (4, 2.5), with vertices roughly at (3,2), (4,1.5), (5,2), (5,3), (4,3.5), (3,3)
Translation: Subtract 3 from x-coordinate.
New coordinates:
- (3-3, 2) = (0, 2)
- (4-3, 1.5) = (1, 1.5)
- (5-3, 2) = (2, 2)
- (5-3, 3) = (2, 3)
- (4-3, 3.5) = (1, 3.5)
- (3-3, 3) = (0, 3)
Draw hexagon shifted 3 units left.
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Problem 4: Translations: 4 right and 3 down.
Original shape: L-shaped polygon with key points like (-5,3), (-4,3), (-4,4), (-3,4), (-3,5), (-2,5), (-2,4), (-1,4), (-1,3), (-2,3), (-2,2), (-3,2), (-3,3), (-4,2), (-4,3)... etc.
Let’s take corner points for simplicity:
Assume original outer corners:
Top-left: (-5, 5) → becomes (-5+4, 5-3) = (-1, 2)
Top-right: (-2, 5) → (2, 2)
Bottom-left: (-5, 2) → (-1, -1)
Bottom-right: (-2, 2) → (2, -1)
Actually, looking at the shape, it's made of blocks. Let’s pick one block’s bottom-left corner: say (-5,2) → moves to (-1,-1). The entire shape shifts accordingly.
We can describe the final position by shifting all points 4 right and 3 down.
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All translations are correctly calculated.
Final Answer:
The shapes should be redrawn on their respective grids after applying the given translations:
- Top-left: Triangle moved 4 units right.
- Top-right: Square moved 3 units right and 2 units down.
- Bottom-left: Hexagon moved 3 units left.
- Bottom-right: L-shape moved 4 units right and 3 units down.
Each new position is determined by adding or subtracting the specified values from the original coordinates.
Parent Tip: Review the logic above to help your child master the concept of translation in geometry worksheet.
