Translations worksheet featuring six exercises where students translate geometric shapes on a coordinate grid according to given directions.

Let’s solve each translation problem step by step.

We are given shapes on a coordinate grid and told how to translate them (move them). A translation means sliding the shape without rotating or flipping it. We move every point of the shape the same number of units left/right and up/down.

Remember:
- Right → add to x-coordinate
- Left → subtract from x-coordinate
- Up → add to y-coordinate
- Down → subtract from y-coordinate

We’ll find the new coordinates for each vertex after the translation, then draw the new shape (but since we’re just solving, we’ll list the new points).

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Problem 1: Translation: 3 right

Original triangle vertices (from graph):
Looking at the green triangle in quadrant III:
- Bottom-left: (-4, -7)
- Top: (-4, -2)
- Bottom-right: (-2, -7)

Move 3 right → add 3 to each x-coordinate:

New points:
- (-4+3, -7) = (-1, -7)
- (-4+3, -2) = (-1, -2)
- (-2+3, -7) = (1, -7)

✔ Final Answer for #1: New vertices at (-1, -7), (-1, -2), (1, -7)

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Problem 2: Translation: 2 right and 3 down

Original quadrilateral (green shape in quadrant II):
Vertices:
- (-5, 5)
- (-2, 5)
- (-2, 3)
- (-4, 3)

Move 2 right → +2 to x
Move 3 down → -3 to y

New points:
- (-5+2, 5-3) = (-3, 2)
- (-2+2, 5-3) = (0, 2)
- (-2+2, 3-3) = (0, 0)
- (-4+2, 3-3) = (-2, 0)

✔ Final Answer for #2: New vertices at (-3, 2), (0, 2), (0, 0), (-2, 0)

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Problem 3: Translation: 5 left

Original triangle (in quadrant IV):
Vertices:
- (1, -8)
- (5, -6)
- (5, -8)

Move 5 left → subtract 5 from x

New points:
- (1-5, -8) = (-4, -8)
- (5-5, -6) = (0, -6)
- (5-5, -8) = (0, -8)

✔ Final Answer for #3: New vertices at (-4, -8), (0, -6), (0, -8)

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Problem 4: Translation: 4 left and 3 down

Original L-shaped figure (in quadrant I):
Vertices (trace the corners):
Start from top-left going clockwise:
- (2, 5)
- (5, 5)
- (5, 3)
- (3, 3)
- (3, 4) ← wait, let me check again — actually looking at the shape:

Actually, better to list all outer corners:
From graph:
Top row: (2,5) to (5,5)
Then down to (5,3)
Left to (3,3)
Up to (3,4)? No — actually it's an L-shape with these key points:

Better approach: The shape has vertices at:
(2,5), (5,5), (5,3), (3,3), (3,4) — but that might be overcomplicating.

Actually, standard way: trace the polygon vertices in order.

Looking carefully:
The green shape is made of two rectangles? Actually, it’s a single polygon with vertices:

Let’s take the 6 corner points as drawn:
Starting from top-left: (2,5) → (5,5) → (5,3) → (3,3) → (3,4) → (2,4) → back to (2,5)? Wait, no — actually from the image, it looks like:

Actually, simpler: the shape has these distinct vertices (corners):

- (2,5)
- (5,5)
- (5,3)
- (3,3)
- (3,4) — this is inside? Hmm.

Wait — perhaps it’s easier to see it as having 6 vertices if you follow the outline:

But to avoid error, let’s use the most obvious corners that define the shape:

Actually, looking at the grid, the shape occupies:

From x=2 to x=5, y=3 to y=5, but missing the bottom-left part? No — it’s an L-shape standing upright.

Standard interpretation: The green shape has vertices at:

(2,5), (5,5), (5,3), (3,3), (3,4), (2,4) — and back to (2,5). But (3,4) to (2,4) is horizontal.

Actually, let’s count the turning points:

Start at (2,5) → right to (5,5) → down to (5,3) → left to (3,3) → up to (3,4) → left to (2,4) → up to (2,5). Yes, that makes sense.

So vertices:
A: (2,5)
B: (5,5)
C: (5,3)
D: (3,3)
E: (3,4)
F: (2,4)

Now apply translation: 4 left (x-4), 3 down (y-3)

New points:
A: (2-4, 5-3) = (-2, 2)
B: (5-4, 5-3) = (1, 2)
C: (5-4, 3-3) = (1, 0)
D: (3-4, 3-3) = (-1, 0)
E: (3-4, 4-3) = (-1, 1)
F: (2-4, 4-3) = (-2, 1)

✔ Final Answer for #4: New vertices at (-2,2), (1,2), (1,0), (-1,0), (-1,1), (-2,1)

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Problem 5: Translation: 4 left and 5 down

Original trapezoid (in quadrant I):
Vertices:
- (1,1)
- (1,4)
- (4,4)
- (3,2) — wait, let’s check the shape.

From graph: It’s a quadrilateral with points:
Bottom-left: (1,1)
Top-left: (1,4)
Top-right: (4,4)
Bottom-right: (3,2) — yes, because it slopes down.

So vertices:
A: (1,1)
B: (1,4)
C: (4,4)
D: (3,2)

Translate: 4 left (x-4), 5 down (y-5)

New points:
A: (1-4, 1-5) = (-3, -4)
B: (1-4, 4-5) = (-3, -1)
C: (4-4, 4-5) = (0, -1)
D: (3-4, 2-5) = (-1, -3)

✔ Final Answer for #5: New vertices at (-3,-4), (-3,-1), (0,-1), (-1,-3)

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Problem 6: Translation: 3 right and 4 up

Original triangle (in quadrant III/IV near origin):
Vertices:
- (-3, -5)
- (-1, -3)
- (0, -5)

Check: From graph, it’s a triangle with base from (-3,-5) to (0,-5), and top at (-1,-3)

Yes.

Translate: 3 right (x+3), 4 up (y+4)

New points:
(-3+3, -5+4) = (0, -1)
(-1+3, -3+4) = (2, 1)
(0+3, -5+4) = (3, -1)

✔ Final Answer for #6: New vertices at (0,-1), (2,1), (3,-1)

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Final Answers Summary:

1) (-1, -7), (-1, -2), (1, -7)
2) (-3, 2), (0, 2), (0, 0), (-2, 0)
3) (-4, -8), (0, -6), (0, -8)
4) (-2,2), (1,2), (1,0), (-1,0), (-1,1), (-2,1)
5) (-3,-4), (-3,-1), (0,-1), (-1,-3)
6) (0,-1), (2,1), (3,-1)

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Final Answer:
1) Vertices: (-1, -7), (-1, -2), (1, -7)
2) Vertices: (-3, 2), (0, 2), (0, 0), (-2, 0)
3) Vertices: (-4, -8), (0, -6), (0, -8)
4) Vertices: (-2, 2), (1, 2), (1, 0), (-1, 0), (-1, 1), (-2, 1)
5) Vertices: (-3, -4), (-3, -1), (0, -1), (-1, -3)
6) Vertices: (0, -1), (2, 1), (3, -1)