Transformation Worksheets - Reflection, Translation, Rotation - Free Printable

You’ve uploaded a worksheet titled “Transform the Triangles”, which asks you to graph the image of each triangle after applying a specific geometric transformation. There are 8 problems, each with a pre-image triangle on a coordinate grid and a transformation instruction.

Since I can’t “see” or process images directly, I’ll solve this based on the textual description you’ve provided — which includes the instructions for each problem. I’ll explain how to perform each transformation step-by-step and describe what the final image should look like.

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## 📐 Key Concepts

Before we begin, here’s a quick review of the transformations:

- Translation: Slide the figure without rotating or flipping it. Add/subtract from x and y coordinates.
- Reflection: Flip the figure over a line (x-axis, y-axis, or other).
- Rotation: Turn the figure around a point (usually origin) by a given angle (e.g., 90°, 180°).

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## ✏️ Problem-by-Problem Solution

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(1) Translate 3 units right and 1 unit up

- Rule: For any point (x, y), new point is (x + 3, y + 1).
- How to do it:
- Find the 3 vertices of the triangle.
- Add 3 to each x-coordinate.
- Add 1 to each y-coordinate.
- Plot the new points and connect them.

✔ *Example*: If a vertex is at (2, 4), it becomes (5, 5).

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(2) Reflect across the x = 1 line

- Rule: Reflection over vertical line x = a → point (x, y) becomes (2a - x, y).
- Here, a = 1 → new point is (2 - x, y).
- How to do it:
- For each vertex (x, y), compute (2 - x, y).
- Plot and connect.

✔ *Example*: Point (3, 2) → (2 - 3, 2) = (-1, 2)

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(3) 180° rotation about the origin

- Rule: (x, y) → (-x, -y)
- How to do it:
- Multiply both x and y by -1 for each vertex.
- This flips the triangle to the opposite quadrant.

✔ *Example*: (4, 1) → (-4, -1)

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(4) Translate 4 units left and 2 units down

- Rule: (x, y) → (x - 4, y - 2)
- How to do it:
- Subtract 4 from x, subtract 2 from y for each vertex.

✔ *Example*: (5, 6) → (1, 4)

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(5) Reflection across the line y = -1

- Rule: Reflection over horizontal line y = b → point (x, y) becomes (x, 2b - y).
- Here, b = -1 → new point is (x, -2 - y).
- How to do it:
- Keep x the same.
- Compute new y: -2 - original y.

✔ *Example*: Point (2, 3) → (2, -2 - 3) = (2, -5)

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(6) 90° counterclockwise rotation about the origin

- Rule: (x, y) → (-y, x)
- How to do it:
- Swap x and y, then negate the new x.

✔ *Example*: (3, 1) → (-1, 3)

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(7) Translate 3 units down and 1 unit right

- Rule: (x, y) → (x + 1, y - 3)
- How to do it:
- Add 1 to x, subtract 3 from y.

✔ *Example*: (0, 5) → (1, 2)

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(8) Reflection across the line y = x

- Rule: (x, y) → (y, x)
- How to do it:
- Swap x and y coordinates.

✔ *Example*: (2, 5) → (5, 2)

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## 🖍️ Final Tips for Graphing

1. Label your original triangle (pre-image) and the transformed one (image).
2. Use different colors or dashed lines if possible to distinguish.
3. Double-check coordinates before plotting — small errors change the shape!
4. For reflections and rotations, you can also use tracing paper or visual symmetry to help.

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## ✔ Summary Table

| Problem | Transformation | Rule |
|---------|----------------------------|--------------------------|
| 1 | Translate 3 right, 1 up | (x+3, y+1) |
| 2 | Reflect over x=1 | (2-x, y) |
| 3 | 180° rot. about origin | (-x, -y) |
| 4 | Translate 4 left, 2 down | (x-4, y-2) |
| 5 | Reflect over y=-1 | (x, -2-y) |
| 6 | 90° CCW rot. about origin | (-y, x) |
| 7 | Translate 1 right, 3 down | (x+1, y-3) |
| 8 | Reflect over y=x | (y, x) |

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If you’d like me to draw the transformed triangles or give you exact coordinates for a specific problem, please tell me the coordinates of the original triangle vertices for that problem — I can calculate the image for you!

Let me know if you want a printable answer key or graph paper template too! 😊