Let’s solve each translation problem step by step.
We are given a triangle on a coordinate grid and told to move it (translate it) according to specific directions: left/right for x-direction, up/down for y-direction.
Remember:
- Moving
right → add to x-coordinate
- Moving
left → subtract from x-coordinate
- Moving
up → add to y-coordinate
- Moving
down → subtract from y-coordinate
We’ll find the new coordinates of each vertex after the translation, then draw or describe the new triangle.
---
Problem 1: Translate 7 units right and 5 units up
Original triangle vertices (from graph):
Let’s label them A, B, C.
Looking at the first graph:
- Point A: (-4, -3)
- Point B: (-2, -3)
- Point C: (-4, 0)
Now translate:
A: (-4 + 7, -3 + 5) = (3, 2)
B: (-2 + 7, -3 + 5) = (5, 2)
C: (-4 + 7, 0 + 5) = (3, 5)
✔ New triangle has vertices at (3,2), (5,2), (3,5)
---
Problem 2: Translate 3 units right and 2 units up
Original triangle vertices:
From second graph:
- A: (1, 1)
- B: (3, 1)
- C: (1, 3)
Translate:
A: (1+3, 1+2) = (4, 3)
B: (3+3, 1+2) = (6, 3)
C: (1+3, 3+2) = (4, 5)
✔ New triangle: (4,3), (6,3), (4,5)
---
Problem 3: Translate 9 units down
This is only vertical — no horizontal movement.
Original triangle vertices (third graph):
- A: (-5, 2)
- B: (-2, 2)
- C: (-5, 5)
Translate down 9 → subtract 9 from y-coordinates:
A: (-5, 2 - 9) = (-5, -7)
B: (-2, 2 - 9) = (-2, -7)
C: (-5, 5 - 9) = (-5, -4)
✔ New triangle: (-5,-7), (-2,-7), (-5,-4)
---
Problem 4: Translate 2 units right and 7 units up
Original triangle (fourth graph):
- A: (-3, -4)
- B: (-1, -4)
- C: (-3, -1)
Translate:
A: (-3+2, -4+7) = (-1, 3)
B: (-1+2, -4+7) = (1, 3)
C: (-3+2, -1+7) = (-1, 6)
✔ New triangle: (-1,3), (1,3), (-1,6)
---
Problem 5: Translate 8 units right and 4 units down
Original triangle (fifth graph):
- A: (-7, 3)
- B: (-4, 3)
- C: (-7, 6)
Translate:
A: (-7+8, 3-4) = (1, -1)
B: (-4+8, 3-4) = (4, -1)
C: (-7+8, 6-4) = (1, 2)
✔ New triangle: (1,-1), (4,-1), (1,2)
---
Problem 6: Translate 2 units right and 7 units up
Wait — this looks identical to Problem 4? Let me check the original image description again.
Actually, looking back — in the user’s image description, problem 6 says: “Translate 2 units right and 7 units up” — same as problem 4? But the starting triangle is different.
In sixth graph:
Original triangle:
- A: (1, -5)
- B: (4, -5)
- C: (1, -2)
Translate:
A: (1+2, -5+7) = (3, 2)
B: (4+2, -5+7) = (6, 2)
C: (1+2, -2+7) = (3, 5)
✔ New triangle: (3,2), (6,2), (3,5)
---
All problems solved.
Final Answer:
1. Vertices: (3,2), (5,2), (3,5)
2. Vertices: (4,3), (6,3), (4,5)
3. Vertices: (-5,-7), (-2,-7), (-5,-4)
4. Vertices: (-1,3), (1,3), (-1,6)
5. Vertices: (1,-1), (4,-1), (1,2)
6. Vertices: (3,2), (6,2), (3,5)
Parent Tip: Review the logic above to help your child master the concept of ttransformation math worksheet.
