Geometry Worksheets | Transformations Worksheets - Free Printable

Since I can't view or access images directly, I’ll help you solve the translation problems based on your description of the worksheet. Each problem involves moving a shape (like a triangle or polygon) on the coordinate plane according to a given translation rule.

Let’s go through each problem step by step. For each, we will:

1. Identify the original coordinates of the vertices of the shape.
2. Apply the translation (move each point accordingly).
3. Plot the new image after translation.

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🔷 General Rule for Translations:

- Right: Add to x-coordinate
- Left: Subtract from x-coordinate
- Up: Add to y-coordinate
- Down: Subtract from y-coordinate

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✔ Problem 1: Translation: 3 right

Original Shape: A green triangle with vertices at approximately:
- A = (-4, -2)
- B = (-4, -6)
- C = (-2, -6)

Translation: 3 units right → Add 3 to each x-coordinate.

New points:
- A' = (-4 + 3, -2) = (-1, -2)
- B' = (-4 + 3, -6) = (-1, -6)
- C' = (-2 + 3, -6) = (1, -6)

✔ Draw a triangle with vertices at (-1, -2), (-1, -6), and (1, -6).

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✔ Problem 2: Translation: 2 right and 3 down

Original Shape: A green quadrilateral (possibly a trapezoid). Let's assume vertices are:
- A = (-4, 2)
- B = (-2, 2)
- C = (-1, 0)
- D = (-4, 0)

Translation: 2 right (+2 to x), 3 down (-3 to y)

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

✔ Draw quadrilateral with vertices: (-2, -1), (0, -1), (1, -3), (-2, -3)

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✔ Problem 3: Translation: 5 left

Original Shape: A green triangle with vertices:
- A = (2, -3)
- B = (4, -3)
- C = (4, -1)

Translation: 5 left → subtract 5 from x

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

✔ Draw triangle at (-3, -3), (-1, -3), (-1, -1)

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✔ Problem 4: Translation: 4 left and 3 down

Original Shape: A green "L"-shaped figure. Let’s assume vertices:
- A = (2, 4)
- B = (2, 3)
- C = (3, 3)
- D = (3, 2)
- E = (4, 2)
- F = (4, 1)

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

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

✔ Draw the L-shape starting at (-2,1) down to (0,-2)

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✔ Problem 5: Translation: 4 left and 5 down

Original Shape: A green curved-like shape (probably a polygon). Let’s say vertices:
- A = (2, 2)
- B = (3, 3)
- C = (4, 2)
- D = (3, 1)

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

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

✔ Connect these points in order to form the translated shape.

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✔ Problem 6: Translation: 3 right and 4 up

Original Shape: A green triangle with vertices:
- A = (-2, -2)
- B = (-1, -1)
- C = (-2, 0)

Translation: 3 right (+3), 4 up (+4)

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

✔ Draw triangle with vertices (1,2), (2,3), (1,4)

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📝 Summary of Steps to Solve Any Translation Problem:

1. Identify the original coordinates of all vertices.
2. Apply the translation rule to each vertex:
- Right: x → x + a
- Left: x → x - a
- Up: y → y + b
- Down: y → y - b
3. Plot the new points and connect them in the same order as the original.
4. Label the image (e.g., A', B', C').

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✔ Final Tips:

- Always move each vertex individually.
- Use graph paper carefully.
- Check that the shape maintains its size and orientation — only position changes.

If you can describe one specific problem in detail (e.g., exact coordinates), I can walk you through it even more precisely!

Let me know if you’d like this turned into a printable answer key or need help drawing it!