📝 Practice Worksheets
Rotate 180 Degrees Around the Origin Rotate 90 Degrees Around the Origin Rotating Objects Around the Origin Rotation Around the Origin Practice
🛠️ Related Tools
🔑 Key Concepts
- A \(180^\circ\) rotation is a half-turn around the origin.
- The coordinate rule is \((x,y)\rightarrow(-x,-y)\).
- Both coordinates change signs, but the order of the coordinates stays the same.
- A \(180^\circ\) rotation is a rigid transformation.
💡 Main Idea
To rotate a triangle \(180^\circ\) around the origin, make each coordinate its opposite. Points in Quadrant I move to Quadrant III, and points in Quadrant III move to Quadrant I.
✏️ Worked Example
🧠 Math Vocabulary
- Rotation: a transformation that turns a figure around a fixed point.
- \(180^\circ\) Rotation: a half-turn around the center of rotation.
- Origin: the point \((0,0)\), where the \(x\)-axis and \(y\)-axis intersect.
- Center of Rotation: the fixed point around which a figure turns.
- Rigid Transformation: a transformation that keeps the same size and shape.
- Image: the new figure after a transformation.
- Preimage: the original figure before a transformation.
- Coordinate Rule: an algebraic rule that shows how ordered pairs change during a transformation.
📚 What You Should Already Know
Students should know how to plot ordered pairs, identify the origin, name the four quadrants, and find opposites of positive and negative numbers.
🚀 What Comes Next
Next, students can compare \(180^\circ\) rotations with \(90^\circ\) clockwise and counterclockwise rotations around the origin.
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