Geometry Worksheets | Transformations Worksheets - Free Printable

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

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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, -6)
- Bottom-right: (-2, -6)
- Top: (-4, -2)

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

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

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

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Problem 2: Translation: 2 right and 3 down

Original quadrilateral vertices (quadrant II):
From graph:
- Top-left: (-5, 5)
- Top-right: (-2, 5)
- Bottom-right: (-2, 3)
- Bottom-left: (-4, 3)

Apply: +2 to x, -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 (quadrant IV):
Vertices:
- Left: (1, -7)
- Right: (5, -5)
- Top: (5, -3)

Wait — let me double-check the graph. Actually, looking again:

The triangle has:
- Bottom-left: (1, -7)
- Bottom-right: (5, -5)
- Top-right: (5, -3)

But actually, from the image, it looks like:
Actually, better to read carefully:

In problem 3, the green triangle is in quadrant IV. Let's pick accurate points:

From grid:
- Point A: (1, -7)
- Point B: (5, -5)
- Point C: (5, -3)

Translation: 5 left → subtract 5 from x

New points:
- (1-5, -7) = (-4, -7)
- (5-5, -5) = (0, -5)
- (5-5, -3) = (0, -3)

✔ Final Answer for #3: New vertices at (-4, -7), (0, -5), (0, -3)

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Problem 4: Translation: 4 left and 3 down

Original L-shape (quadrant I):

Vertices (let’s trace the corners):

Start from top-left of L:
- (2, 5)
- (4, 5)
- (4, 4)
- (5, 4)
- (5, 2)
- (2, 2) ← back? Wait, better to list all unique corner points.

Actually, from graph:

It’s an L made of squares. Corners:

Top row: (2,5), (3,5), (4,5)
Then down: (4,4), (4,3), (4,2)
Then left: (3,2), (2,2)

So key vertices (outer corners):
- (2,5)
- (4,5)
- (4,2)
- (2,2)

But to be precise, let’s take all turning points:

Actually, for translation, we can take any set of defining points. Let’s use:

Points: (2,5), (4,5), (4,2), (2,2)

Translate: 4 left (x-4), 3 down (y-3)

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

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

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Problem 5: Translation: 4 left and 5 down

Original trapezoid (quadrant I):

Vertices from graph:
- (1, 1)
- (3, 1)
- (4, 3)
- (2, 4)

Check: yes, that matches the green shape.

Translate: x-4, y-5

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

✔ Final Answer for #5: New vertices at (-3, -4), (-1, -4), (0, -2), (-2, -1)

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Problem 6: Translation: 3 right and 4 up

Original triangle (quadrant III/IV):

Vertices:
- (-3, -5)
- (-1, -6)
- (0, -2)

Wait — let’s check the graph.

Actually, from image:

Green triangle spans from x=-3 to x=0, y=-6 to y=-2.

Points:
- Left-bottom: (-3, -5)? Wait no.

Better:

Looking at grid:

Point A: (-3, -5) — but wait, bottom point is at (-1, -6)

Actually:

From graph:
- Vertex 1: (-3, -5)
- Vertex 2: (-1, -6)
- Vertex 3: (0, -2)

Yes.

Translate: +3 to x, +4 to y

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

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

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Final Answers Summary:

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

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