Rotation Worksheets - Free Printable

The task involves rotating points on a coordinate grid by specific angles (90°, 180°, or 270°) either clockwise or counterclockwise about the origin. Below is a detailed explanation of how to solve such problems, along with the general rules for rotations.

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General Rules for Rotations About the Origin

1. 90° Counterclockwise Rotation:
- If the original point is \((x, y)\), the new coordinates after rotation will be \((-y, x)\).

2. 90° Clockwise Rotation:
- If the original point is \((x, y)\), the new coordinates after rotation will be \((y, -x)\).

3. 180° Rotation (Clockwise or Counterclockwise):
- If the original point is \((x, y)\), the new coordinates after rotation will be \((-x, -y)\).

4. 270° Counterclockwise Rotation:
- This is equivalent to a 90° clockwise rotation.
- If the original point is \((x, y)\), the new coordinates after rotation will be \((y, -x)\).

5. 270° Clockwise Rotation:
- This is equivalent to a 90° counterclockwise rotation.
- If the original point is \((x, y)\), the new coordinates after rotation will be \((-y, x)\).

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Steps to Solve the Problem

1. Identify the original coordinates of the point.
2. Determine the type of rotation (90°, 180°, or 270°) and its direction (clockwise or counterclockwise).
3. Apply the appropriate rotation rule to find the new coordinates.
4. Plot the new coordinates on the grid.

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Example Problem

Let's solve one of the problems from the worksheet as an example:

#### Problem:
Rotate the point \((3, 2)\) 90° counterclockwise about the origin.

#### Solution:
1. Original Coordinates: \((3, 2)\)
2. Rotation Type: 90° counterclockwise
3. Apply the Rule:
- For a 90° counterclockwise rotation, the new coordinates are \((-y, x)\).
- Here, \(x = 3\) and \(y = 2\).
- So, the new coordinates are \((-2, 3)\).

4. Plot the Point:
- The new point \((-2, 3)\) is located two units to the left of the origin and three units above it.

#### Final Answer:
The rotated point is \(\boxed{(-2, 3)}\).

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Additional Examples

Here are a few more examples to illustrate the process:

1. Rotate \((4, -1)\) 180° about the origin:
- Original coordinates: \((4, -1)\)
- Rotation rule for 180°: \((-x, -y)\)
- New coordinates: \((-4, 1)\)

2. Rotate \((-2, 5)\) 270° clockwise about the origin:
- Original coordinates: \((-2, 5)\)
- Rotation rule for 270° clockwise: \((-y, x)\)
- New coordinates: \((-5, -2)\)

3. Rotate \((0, 6)\) 90° clockwise about the origin:
- Original coordinates: \((0, 6)\)
- Rotation rule for 90° clockwise: \((y, -x)\)
- New coordinates: \((6, 0)\)

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Final Answer Format

For each problem, the final answer should be written in the format \(\boxed{(x, y)}\), where \((x, y)\) are the coordinates of the rotated point.

If you need solutions for specific problems from the worksheet, please let me know!