ROTASI (PERPUTARAN) || TRANSFORMASI GEOMETRI

Introduction

This tutorial will explore the concept of rotation in geometry. Rotation, or "perputaran" in Indonesian, is a fundamental transformation that involves turning a shape around a fixed point. Understanding rotation is essential for students, particularly for those in grade 9, as it has practical applications in daily life and advanced mathematics.

Step 1: Understanding the Basics of Rotation

• Definition: Rotation refers to turning a figure around a specific point called the center of rotation.
• Key components:
  • Center of rotation: The fixed point around which the rotation occurs.
  • Angle of rotation: The degree to which the figure is turned (e.g., 90°, 180°, 270°).
  • Direction: Rotation can occur clockwise or counterclockwise.

Practical Tip

To visualize rotation, use a simple object like a clock. The hands of the clock rotate around the center, illustrating the concept of rotation effectively.

Step 2: Identifying Real-Life Examples of Rotation

• Think about common objects and actions that involve rotation:
  • Clock hands: Move around the center point to indicate time.
  • Ferris wheels: Rotate around a central axis.
  • Spinning tops: Rotate around their base.

Common Pitfall

Avoid confusing rotation with other transformations, such as reflection (flipping a shape over a line) or translation (sliding a shape from one position to another).

Step 3: Performing a Rotation on a Coordinate Plane

• Choose a point: Start with a point on the coordinate plane, say (x, y).
• Select the center of rotation: For example, choose the origin (0, 0).
• Decide the angle and direction of rotation.
• Use rotation formulas based on the angle:
  • For 90° clockwise: (x, y) transforms to (y, -x).
  • For 180°: (x, y) transforms to (-x, -y).
  • For 90° counterclockwise: (x, y) transforms to (-y, x).

Example Calculation

1. Rotate the point (3, 4) 90° clockwise around the origin:
   • New coordinates: (4, -3).

Step 4: Practice Problems

• Attempt to rotate the following points around the origin:
  • (1, 2) by 180°
  • (5, 5) by 90° counterclockwise
• Check your answers using the rotation formulas provided.

Conclusion

Rotation is a fundamental aspect of geometry with numerous real-world applications. By understanding the key concepts, identifying practical examples, and practicing rotation on a coordinate plane, you will build a solid foundation in this topic. As you continue your studies, consider exploring other transformations such as reflection and translation for a well-rounded understanding of geometry. Happy learning!