Transformasi (4) - Transformasi Rotasi, Rumus Tranformasi Rotasi, Soal Rotasi - Matematika SMP

Introduction

This tutorial focuses on the concept of rotation transformations in geometry, particularly for 9th-grade mathematics. It will guide you through the fundamental principles of rotation, the formulas involved, and practice problems to enhance your understanding. Mastering these concepts is essential for solving geometric problems and enhances your mathematical skills.

Step 1: Understanding Rotation Transformations

• Definition: A rotation transformation involves turning a figure around a fixed point, known as the center of rotation.
• Degrees of Rotation: Common degrees for rotation include:
  • 90 degrees
  • 180 degrees
  • 270 degrees
  • 360 degrees
• Direction: Rotations can be clockwise or counterclockwise.

Practical Tip

• Visualize the rotation by drawing the original figure and its rotated position on graph paper to see how the points change.

Step 2: Learning the Rotation Formula

• The rotation formulas depend on the angle and the center of rotation. For a point ( P(x, y) ) rotated around the origin ( O(0, 0) ):
  • 90 degrees counterclockwise:
    • New coordinates: ( P'(-y, x) )
  • 180 degrees:
    • New coordinates: ( P'(-x, -y) )
  • 270 degrees counterclockwise (or 90 degrees clockwise):
    • New coordinates: ( P'(y, -x) )

Example Calculation

• For a point ( P(2, 3) ) rotated 90 degrees counterclockwise:
  • New coordinates: ( P'(-3, 2) )

Step 3: Applying Rotation to Solve Problems

• Step-by-step approach:
  1. Identify the point or shape you want to rotate.
  2. Determine the angle and direction of rotation.
  3. Use the appropriate rotation formula based on the angle.
  4. Calculate the new coordinates.

Example Problem

• Rotate point ( A(4, 1) ) 180 degrees about the origin.
  • New coordinates: ( A'(-4, -1) )

Step 4: Practice with Additional Problems

• Try rotating the following points:
  • Point ( B(1, 2) ) 90 degrees counterclockwise.
  • Point ( C(-3, 3) ) 270 degrees counterclockwise.

Common Pitfalls

• Forgetting to consider the direction of rotation.
• Mixing up the formulas for different angles.

Conclusion

In this tutorial, you have learned about rotation transformations, the related formulas, and how to apply them to solve geometric problems. To further your understanding, practice additional rotation problems and familiarize yourself with different figures. This foundational knowledge will be beneficial as you progress in geometry and related mathematical concepts.