Rotate a Triangle 90 Degrees Clockwise Around the Origin

🔑 Key Concepts

  • A \(90^\circ\) clockwise rotation turns a figure right around the origin.
  • The coordinate rule is \((x,y)\rightarrow(y,-x)\).
  • The \(x\)- and \(y\)-values switch places.
  • The new \(y\)-value becomes the opposite of the original \(x\)-value.

💡 Main Idea

To rotate a point \(90^\circ\) clockwise around the origin, use the rule \((x,y)\rightarrow(y,-x)\). This moves the triangle from Quadrant II to Quadrant I in this example.

✏️ Worked Example

🧠 Math Vocabulary

  • Rotation: a transformation that turns a figure around a fixed point.
  • \(90^\circ\) Clockwise Rotation: a quarter-turn to the right 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 understand positive and negative coordinate values.

🚀 What Comes Next

Next, students can compare \(90^\circ\) clockwise rotations with \(90^\circ\) counterclockwise rotations and \(180^\circ\) rotations around the origin.

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