📝 Practice Worksheets
🛠️ Related Tools
🔑 Key Concepts
- A rotation turns a figure around a fixed point called the center of rotation.
- In this lesson, the center of rotation is the origin, \((0,0)\).
- A \(180^\circ\) rotation around the origin moves every point to the opposite quadrant.
- The coordinate rule for a \(180^\circ\) rotation around the origin is \((x,y)\rightarrow(-x,-y)\).
- A rotation is a rigid transformation because the image keeps the same size and shape.
✏️ Worked Examples
🧠 Math Vocabulary
- Rotation: a transformation that turns a figure around a fixed point.
- Center of Rotation: the fixed point around which a figure turns.
- Origin: the point \((0,0)\) where the \(x\)-axis and \(y\)-axis intersect.
- \(180^\circ\) Rotation: a half-turn around the center of rotation.
- Rigid Transformation: a transformation that preserves 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 each ordered pair changes during a transformation.
- Corresponding Points: matching points on the preimage and image, such as \(A\) and \(A'\).
💡 Main Idea
A \(180^\circ\) rotation around the origin sends every point to the opposite side of the origin. Both coordinates change signs, so the rule is \((x,y)\rightarrow(-x,-y)\).
📚 What You Should Already Know
Students should know how to plot ordered pairs, identify quadrants, locate the origin, and find opposites of positive and negative numbers.
🚀 What Comes Next
After practicing \(180^\circ\) rotations, students can compare clockwise and counterclockwise \(90^\circ\) rotations and use coordinate rules to rotate figures around the origin.
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