📝 Practice Worksheets
Rotate 180° Around Origin Rotate 90° Around Origin 90° and 180° Rotations Rotation Around Origin Rotation Practice
🛠️ Related Tool
Rotation Explorer🔑 Key Concepts
- When the center of rotation is not the origin, first translate the center of rotation to the origin.
- Apply the standard rotation rule around the origin.
- For a \(90^\circ\) clockwise rotation around the origin, use \((x,y)\rightarrow(y,-x)\).
- After rotating, translate the figure back to the original center of rotation.
- Rotations preserve shape and size, so the image is congruent to the original figure.
✏️ Worked Examples
🧠 Math Vocabulary
- Rotation: A transformation that turns a figure around a fixed point.
- Center of rotation: The fixed point that a figure rotates around.
- Clockwise: A turn in the same direction as the hands of a clock.
- Preimage: The original figure before a transformation.
- Image: The new figure after a transformation.
- Congruent figures: Figures with the same size and same shape.
💡 Main Idea
To rotate around a point that is not the origin, temporarily shift the center of rotation to the origin, apply the rotation rule, and then shift the rotated figure back.
📚 What You Should Already Know
Students should know how to plot points, identify coordinates, translate points on the coordinate plane, and use basic rotation rules around the origin.
🚀 What Comes Next
Students can extend this process to other centers of rotation, counterclockwise rotations, \(180^\circ\) rotations, and combinations of transformations on the coordinate plane.
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