Rotation Worksheets - Free Printable

Let’s solve each rotation problem step by step. We’ll use the rules for rotating points around the origin (0,0) on a coordinate plane.

Here are the key rotation rules you need to remember:

- 90° clockwise: (x, y) → (y, -x)
- 90° counterclockwise: (x, y) → (-y, x)
- 180° (either direction): (x, y) → (-x, -y)
- 270° clockwise = same as 90° counterclockwise: (x, y) → (-y, x)
- 270° counterclockwise = same as 90° clockwise: (x, y) → (y, -x)

We will apply these rules to each quadrilateral in the worksheet. Since we don’t have exact coordinates from the image, I’ll assume standard positions based on typical problems like this — but if your graph has different coordinates, plug those into the same rules!

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Problem 1: 180° rotation

Assume original shape has vertices at:
A(1,1), B(3,1), C(3,3), D(1,3) — a small square in quadrant I.

Apply 180° rule: (x,y) → (-x,-y)

New points:
A’(-1,-1), B’(-3,-1), C’(-3,-3), D’(-1,-3)

→ Draw the square in quadrant III.

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Problem 2: 90° clockwise rotation

Same original square: A(1,1), B(3,1), C(3,3), D(1,3)

Rule: (x,y) → (y, -x)

A’(1, -1), B’(1, -3), C’(3, -3), D’(3, -1)

→ This forms a square in quadrant IV.

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Problem 3: 90° counterclockwise rotation

Original triangle? Let’s say vertices at: A(0,0), B(2,0), C(1,-2) — pointing down.

Rule: (x,y) → (-y, x)

A’(0,0), B’(0,2), C’(2,1)

→ Now it points right, in quadrant I.

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Problem 4: 180° rotation

Say trapezoid with points: A(1,1), B(3,1), C(2,3), D(0,3)

Apply 180°: (x,y) → (-x,-y)

A’(-1,-1), B’(-3,-1), C’(-2,-3), D’(0,-3)

→ Flipped to bottom left.

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Problem 5: 90° counterclockwise rotation

Triangle: A(0,0), B(2,0), C(0,2) — right triangle in QI

Rule: (x,y) → (-y,x)

A’(0,0), B’(0,2), C’(-2,0)

→ Now in QII, pointing left.

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Problem 6: 90° clockwise/counterclockwise rotation

Wait — “90° clockwise/counterclockwise” is confusing. Probably means choose one? Or maybe it's a typo and should be just one direction.

If it says “clockwise”, use (x,y) → (y,-x)

If “counterclockwise”, use (x,y) → (-y,x)

Assume it’s 90° clockwise for consistency.

Original pentagon? Let’s pick simple points: A(1,0), B(2,1), C(1,2), D(0,2), E(0,1)

Apply 90° CW: (x,y) → (y,-x)

A’(0,-1), B’(1,-2), C’(2,-1), D’(2,0), E’(1,0)

→ Rotated to lower right.

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Problem 7: 180° rotation

Another triangle? Say A(1,2), B(3,2), C(2,4)

180° → (-x,-y)

A’(-1,-2), B’(-3,-2), C’(-2,-4)

→ Bottom left.

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Problem 8: 90° clockwise rotation

Last one — maybe a kite or arrow shape.

Points: A(0,1), B(1,2), C(2,1), D(1,0)

90° CW: (x,y) → (y,-x)

A’(1,0), B’(2,-1), C’(1,-2), D’(0,-1)

→ Points downward now.

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✔ Final Check: All rotations follow the correct transformation rules. Each point was moved according to its rotation type. Shapes keep their size and shape — only position and orientation change.

Final Answer:
For each problem, rotate every vertex using the correct rule:
- 90° CW: (x,y) → (y, -x)
- 90° CCW: (x,y) → (-y, x)
- 180°: (x,y) → (-x, -y)

Draw the new shape using the rotated points. The final answer is the set of correctly rotated graphs for all 8 problems as described above.