Practice worksheet for students to identify different types of geometric transformations such as translations, reflections, rotations, and dilations using coordinate graphs.

Let's go through each of the 9 graphs and determine the type of transformation shown. We'll analyze each one step by step based on the positions of the original figure and its image (the primed version, like A', B', etc.).

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1. Triangle ABC → Triangle A'B'C'

- Original triangle ABC is in the third quadrant.
- Image triangle A'B'C' is in the first quadrant.
- The orientation appears flipped across the y-axis.
- Each point is reflected over the y-axis.

✔ Transformation: Reflection over the y-axis

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2. Quadrilateral MNO → M'N'O'

- Points:
- M → M': same position
- N → N': moved right and up
- O → O': moved right and up
- All points have been shifted right by 3 units and up by 1 unit.
- Shape and size are preserved.

✔ Transformation: Translation (Translation)
→ Specifically: (x + 3, y + 1)

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3. Segment PQ → P'Q'

- Original segment PQ is in the third quadrant.
- Image P'Q' is in the first quadrant.
- The segment has been rotated around the origin.
- It looks like it’s been turned 90 degrees counterclockwise.
- Check: If you rotate PQ 90° CCW about the origin, it matches P'Q'.

✔ Transformation: Rotation 90° counterclockwise about the origin

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4. Quadrilateral ABCD → A'B'C'D'

- Original quadrilateral is above the x-axis.
- Image A'B'C'D' is below the x-axis.
- The shape is mirrored vertically.
- Looks like a reflection over the x-axis.

✔ Transformation: Reflection over the x-axis

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5. Triangle DEF → D'E'F'

- Original triangle is on the left side.
- Image is on the right side, with same shape and size.
- The direction from D to E to F is reversed in the image.
- This suggests a reflection over the y-axis or a rotation?

Wait: Let’s check coordinates roughly:

- D ≈ (-3, 1), D' ≈ (3, 1)
- E ≈ (-1, 3), E' ≈ (1, 3)
- So each point has opposite x-coordinate, same y.

✔ Transformation: Reflection over the y-axis

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6. Triangle JKL → J'K'L'

- Original triangle JKL is in the second quadrant.
- Image J'K'L' is smaller and inside the original triangle.
- The image shares vertex J = J'.
- K' and L' are closer to J than K and L.
- This is a dilation centered at J (origin?) but not at origin.

Wait: J is at (-2, 0), J' is at (-2, 0) — same point.

Check distances:
- From J to K: horizontal distance ~4 units
- From J to K': ~2 units → half

So scaling factor = ½, centered at J.

✔ Transformation: Dilation with scale factor ½ centered at point J

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7. Triangle ABC → A'B'C'

- Original triangle ABC is in the fourth quadrant.
- Image A'B'C' is in the second quadrant.
- The triangle appears to be rotated 180 degrees about the origin.
- Each point is directly opposite through the origin.

Example:
- A ≈ (-3, -2), A' ≈ (3, 2)
- B ≈ (-1, -1), B' ≈ (1, 1)
- C ≈ (-2, 0), C' ≈ (2, 0)

Each coordinate is negated: (x, y) → (-x, -y)

✔ Transformation: Rotation 180° about the origin

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8. Trapezoid GHIJ → G'H'I'J'

- Original trapezoid is on the left side.
- Image is on the right side.
- Orientation is flipped: top and bottom switched?
- But wait: G → G', H → H', I → I', J → J'
- G and H are on top, G' and H' are on top? No — actually, G' and H' are on the bottom.
- Wait: look carefully — the image is upside down and flipped.

But notice:
- G ≈ (-2, 3), G' ≈ (2, -3)
- H ≈ (-1, 3), H' ≈ (1, -3)
- I ≈ (-3, 0), I' ≈ (3, 0)
- J ≈ (0, 0), J' ≈ (0, 0)

Wait — J is at origin, J' is also at origin.

So every point (x, y) → (-x, -y)? That would be 180° rotation.

But G(-2,3) → G'(2,-3): yes, that's (x,y) → (-x,-y)

Similarly, H(-1,3) → H'(1,-3)

I(-3,0) → I'(3,0)

J(0,0) → J'(0,0)

✔ Transformation: Rotation 180° about the origin

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9. Line segment MP → M'P'

- Original line segment MP goes from upper-left to lower-right.
- Image M'P' goes from upper-right to lower-left.
- They intersect at point N (which is N'), suggesting a center of symmetry.
- The two lines cross at the origin.
- M → M', P → P', and N is fixed.

Looks like a reflection over the origin, but that's not standard.

Wait: Actually, this looks like a rotation 180° about the origin.

Because:
- M ≈ (-3, 2), M' ≈ (3, -2)
- P ≈ (-2, -3), P' ≈ (2, 3)
- N ≈ (0, 0), N' ≈ (0, 0)

So again: (x, y) → (-x, -y)

✔ Transformation: Rotation 180° about the origin

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✔ Final Answers:

| Number | Transformation |
|--------|----------------|
| 1 | Reflection over the y-axis |
| 2 | Translation (right 3, up 1) |
| 3 | Rotation 90° counterclockwise about the origin |
| 4 | Reflection over the x-axis |
| 5 | Reflection over the y-axis |
| 6 | Dilation with scale factor ½ centered at point J |
| 7 | Rotation 180° about the origin |
| 8 | Rotation 180° about the origin |
| 9 | Rotation 180° about the origin |

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📝 Summary of Transformations:

- Reflection: Flips over a line (x-axis, y-axis).
- Rotation: Turns around a point (often origin).
- Translation: Slides without turning.
- Dilation: Enlarges or shrinks from a center point.

Let me know if you'd like these written out clearly for the worksheet!