Translations worksheet with six problems involving moving shapes on a coordinate plane.

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 of the shape after the translation, then draw the translated shape (but since we’re solving numerically, we’ll list the new vertices).

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Problem 1: Translation: 3 right

Original shape is a triangle with vertices at:
Looking at the graph:
- Bottom-left: (-4, -5)
- Bottom-right: (-2, -5)
- Top: (-4, -2)

Translate 3 right → add 3 to each x-coordinate.

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

✔ Final Answer for #1: New vertices at (-1, -5), (1, -5), (-1, -2)

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Problem 2: Translation: 2 right and 3 down

Original quadrilateral vertices (from graph):
- Top-left: (-4, 4)
- Top-right: (-2, 4)
- Bottom-right: (-2, 2)
- Bottom-left: (-4, 3) ← wait, let me check again — actually looking carefully:

Actually, from the image:
It looks like a trapezoid with points:
- (-4, 4)
- (-2, 4)
- (-2, 2)
- (-3, 3) ? Wait — better to count grid.

Wait — let's be precise. From the graph in problem 2:

Points appear to be:
A: (-4, 4)
B: (-2, 4)
C: (-2, 2)
D: (-3, 3) — but that doesn’t look right. Actually, looking again — it might be:

Actually, standard way: Let’s assume the four corners are:
(-4, 4), (-2, 4), (-2, 2), and (-4, 3)? No — let me re-express.

Better approach: Since it’s a polygon, pick all visible vertices.

From the green shape in #2:
Top edge from x=-4 to x=-2 at y=4 → so points (-4,4) and (-2,4)
Then down to (-2,2)
Then diagonally? Or straight? Actually, from (-2,2) to (-4,3)? That would make a slanted side.

Wait — perhaps it’s a quadrilateral with vertices:
P1: (-4, 4)
P2: (-2, 4)
P3: (-2, 2)
P4: (-4, 3) — yes, that matches the drawing.

Now translate: 2 right → +2 to x; 3 down → -3 to y.

New points:
P1: (-4+2, 4-3) = (-2, 1)
P2: (-2+2, 4-3) = (0, 1)
P3: (-2+2, 2-3) = (0, -1)
P4: (-4+2, 3-3) = (-2, 0)

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

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Problem 3: Translation: 5 left

Original triangle vertices (from graph):
Looks like:
- (1, -6)
- (4, -5)
- (4, -7)

Check: bottom-right at (4,-7), top at (4,-5), left at (1,-6) — yes.

Translate 5 left → subtract 5 from each x.

New points:
(1-5, -6) = (-4, -6)
(4-5, -5) = (-1, -5)
(4-5, -7) = (-1, -7)

✔ Final Answer for #3: New vertices at (-4, -6), (-1, -5), (-1, -7)

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Problem 4: Translation: 4 left and 3 down

Original shape — looks like an L-shape or irregular quadrilateral.

Vertices from graph:
Start from top-left: (2, 4)
Then (4, 4)
Then (4, 2)
Then (3, 2)
Then (3, 3)? Wait — let’s trace:

Actually, from the green shape:
- (2, 4)
- (4, 4)
- (4, 2)
- (3, 2)
- (3, 3) — no, that might not be closed.

Wait — better: It appears to have 5 points? Or maybe 4?

Looking closely: It’s a polyomino-like shape.

Assume vertices in order:
A: (2, 4)
B: (4, 4)
C: (4, 2)
D: (3, 2)
E: (3, 3) — but then back to A? Not quite.

Actually, perhaps it’s drawn as:
From (2,4) to (4,4) to (4,2) to (3,2) to (3,3) to (2,3) to (2,4)? Too many.

Wait — simpler: The shape has outer corners at:
(2,4), (4,4), (4,2), (3,2), and (3,3) is inside? No.

I think it’s a pentagon? But let’s count the green lines.

Actually, from the image, it’s likely these key points:
- (2, 4)
- (4, 4)
- (4, 2)
- (3, 2)
- (3, 3) — but (3,3) connects to (2,3)? And (2,3) to (2,4)?

This is getting messy. Let me define the minimal set of vertices that define the shape.

Alternatively, since it’s a translation, we can take any point and move it, but to be accurate, let’s list all corner points.

Upon careful inspection of problem 4 graph:

The green shape has vertices at:
1. (2, 4)
2. (4, 4)
3. (4, 2)
4. (3, 2)
5. (3, 3)
6. (2, 3) — and back to (2,4)

So six points? But (3,3) to (2,3) to (2,4) closes it.

But actually, (2,3) to (2,4) is vertical, and (2,4) to (4,4) horizontal, etc.

To simplify, let’s take the distinct corners:

List:
A: (2,4)
B: (4,4)
C: (4,2)
D: (3,2)
E: (3,3)
F: (2,3)

Now translate each: 4 left → x-4; 3 down → y-3

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

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

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Problem 5: Translation: 4 left and 5 down

Original quadrilateral vertices (from graph):
Looks like:
- (1, 2)
- (3, 2)
- (3, 4)
- (1, 3) — wait, let's see.

Actually, from the green shape:
Bottom-left: (1,2)
Bottom-right: (3,2)
Top-right: (3,4)
Top-left: (1,3) — yes, that makes a trapezoid.

Translate: 4 left → x-4; 5 down → y-5

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

✔ Final Answer for #5: New vertices at (-3,-3), (-1,-3), (-1,-1), (-3,-2)

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Problem 6: Translation: 3 right and 4 up

Original triangle vertices (from graph):
Looks like:
- (-3, -5)
- (-1, -4)
- (-1, -6)

Check: leftmost at (-3,-5), then two points at x=-1: y=-4 and y=-6.

Yes.

Translate: 3 right → x+3; 4 up → y+4

New points:
(-3+3, -5+4) = (0, -1)
(-1+3, -4+4) = (2, 0)
(-1+3, -6+4) = (2, -2)

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

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Final Answers Summary:

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

Note: For problems where the shape has more than 3 or 4 points, I included all vertices that define the outline. In practice, students would plot these new points and connect them in the same order as the original.

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