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 in the specified direction.

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 translated shape (though since we’re solving numerically, we’ll just 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, -5)
- Bottom-right: (-2, -5)
- Top: (-4, -1)

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

- (-4 + 3, -5) = (-1, -5)
- (-2 + 3, -5) = (1, -5)
- (-4 + 3, -1) = (-1, -1)

New vertices: (-1, -5), (1, -5), (-1, -1)

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Problem 2: Translation: 2 right and 3 down

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

Apply translation: +2 to x, -3 to y

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

New vertices: (-3, 1), (-1, 1), (0, -1), (-2, -1)

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Problem 3: Translation: 5 left

Original triangle (in quadrant IV):
Vertices:
- (1, -6)
- (5, -4)
- (5, -7)

Move 5 left → subtract 5 from x:

- (1-5, -6) = (-4, -6)
- (5-5, -4) = (0, -4)
- (5-5, -7) = (0, -7)

New vertices: (-4, -6), (0, -4), (0, -7)

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Problem 4: Translation: 4 left and 3 down

Original L-shaped figure (quadrant I):
Vertices (trace the corners):
Start from top-left: (2, 5)
Then: (4, 5), (4, 3), (5, 3), (5, 2), (2, 2) — wait, let's check carefully.

Actually, looking at the green shape:
It looks like:
- (2, 5)
- (4, 5)
- (4, 3)
- (5, 3)
- (5, 2)
- (2, 2) — but that might not be closed properly.

Wait — better to pick key points. Let’s take the outer corners:

From the drawing, it seems to have these vertices (going clockwise):
(2,5), (4,5), (4,3), (5,3), (5,2), (2,2) — yes, that makes an L-shape.

Now apply: -4 to x, -3 to y

- (2-4, 5-3) = (-2, 2)
- (4-4, 5-3) = (0, 2)
- (4-4, 3-3) = (0, 0)
- (5-4, 3-3) = (1, 0)
- (5-4, 2-3) = (1, -1)
- (2-4, 2-3) = (-2, -1)

New vertices: (-2, 2), (0, 2), (0, 0), (1, 0), (1, -1), (-2, -1)

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Problem 5: Translation: 4 left and 5 down

Original trapezoid (quadrant I):
Vertices:
- (1, 1)
- (1, 4)
- (4, 4)
- (3, 2)

Apply: -4 to x, -5 to y

- (1-4, 1-5) = (-3, -4)
- (1-4, 4-5) = (-3, -1)
- (4-4, 4-5) = (0, -1)
- (3-4, 2-5) = (-1, -3)

New vertices: (-3, -4), (-3, -1), (0, -1), (-1, -3)

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Problem 6: Translation: 3 right and 4 up

Original triangle (quadrant III/IV near origin):
Vertices:
- (-3, -3)
- (-1, -1)
- (-2, -4)

Apply: +3 to x, +4 to y

- (-3+3, -3+4) = (0, 1)
- (-1+3, -1+4) = (2, 3)
- (-2+3, -4+4) = (1, 0)

New vertices: (0, 1), (2, 3), (1, 0)

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Final Answer:

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