Rotate a Triangle 90 Degrees Counterclockwise Around the Origin

🔑 Key Concepts

  • A \(90^\circ\) counterclockwise rotation turns a figure left around the origin.
  • The coordinate rule is \((x,y)\rightarrow(-y,x)\).
  • The \(x\)- and \(y\)-values switch places during a \(90^\circ\) rotation.
  • A rotation is a rigid transformation because size and shape stay the same.

💡 Main Idea

To rotate a point \(90^\circ\) counterclockwise around the origin, switch the coordinates and make the new \(x\)-coordinate the opposite of the original \(y\)-coordinate. The rule is \((x,y)\rightarrow(-y,x)\).

✏️ Worked Example

🧠 Math Vocabulary

  • Rotation: a transformation that turns a figure around a fixed point.
  • Center of Rotation: the point a figure rotates around.
  • Origin: the point \((0,0)\), where the \(x\)-axis and \(y\)-axis intersect.
  • Counterclockwise: turning in the opposite direction of the hands of a clock.
  • 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 \(90^\circ\) counterclockwise rotations with \(90^\circ\) clockwise rotations, \(180^\circ\) rotations, reflections, translations, and dilations.

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