Let’s solve each translation problem step by step.
---
Problem 1: Translations — 4 right
Original shape: A triangle with vertices at approximately (-5, -4), (-3, -4), and (-4, -3).
(We can pick any point — let’s use the bottom-left corner: (-5, -4))
To translate
4 units right, we add 4 to the x-coordinate:
New x = -5 + 4 = -1
y stays the same → -4
So new position of that point: (-1, -4)
Do this for all points:
- (-5, -4) → (-1, -4)
- (-3, -4) → (1, -4)
- (-4, -3) → (0, -3)
✔ The translated triangle will be centered around x=0 to x=1, y=-3 to y=-4.
---
Problem 2: Translations — 3 right and 2 down
Original shape: A square with corners at (-4, 3), (-3, 3), (-3, 4), (-4, 4)
Apply translation:
- Add 3 to x → move right
- Subtract 2 from y → move down
Take top-left corner (-4, 3):
→ x: -4 + 3 = -1
→ y: 3 - 2 = 1
New point: (-1, 1)
All points:
- (-4, 3) → (-1, 1)
- (-3, 3) → (0, 1)
- (-3, 4) → (0, 2)
- (-4, 4) → (-1, 2)
✔ Square now sits between x=-1 to 0, y=1 to 2.
---
Problem 3: Translations — 3 left
Original shape: Hexagon centered near (4, 2.5). Let’s take a vertex: (5, 2)
Translate 3 left → subtract 3 from x:
New x = 5 - 3 = 2
y stays 2 → (2, 2)
Another point: (4, 3) → (1, 3)
Another: (3, 2) → (0, 2)
✔ Hexagon moves left — now centered around x=1 to x=2.
---
Problem 4: Translations — 4 right and 3 down
Original shape: L-shaped figure. Let’s pick key points:
Top-right corner: (-2, 5)
Bottom-left corner: (-5, 2)
Apply:
- x += 4 → move right
- y -= 3 → move down
(-2, 5) → (2, 2)
(-5, 2) → (-1, -1)
Other points:
- (-5, 3) → (-1, 0)
- (-5, 4) → (-1, 1)
- (-4, 5) → (0, 2)
- (-3, 5) → (1, 2)
- (-3, 4) → (1, 1)
- (-3, 3) → (1, 0)
✔ Shape moves to the right and down — now mostly in quadrant IV and III.
---
Since the user did not request explanation, teaching, or practice tasks, we only provide the final answer as per instructions.
Final Answer:
The shapes are translated as follows:
1. Triangle moved 4 units right → new positions: (-1,-4), (1,-4), (0,-3)
2. Square moved 3 right, 2 down → new positions: (-1,1), (0,1), (0,2), (-1,2)
3. Hexagon moved 3 left → new positions include (2,2), (1,3), (0,2)
4. L-shape moved 4 right, 3 down → new positions include (2,2), (-1,-1), (-1,0), (0,2), etc.
Parent Tip: Review the logic above to help your child master the concept of translations in geometry worksheet.
