Matematika kelas 9 : Transformasi Geometri (part 3 : Rotasi I)

Introduction

This tutorial focuses on the concept of rotation in geometry, specifically for a center of rotation at the origin (0,0). Understanding this concept is essential for students in grade 9 as it builds a foundation for more advanced topics in geometry and transformations.

Step 1: Understanding Rotation

• Rotation involves turning a figure around a fixed point known as the center of rotation.
• In this tutorial, the center of rotation is the origin (0,0).
• The rotation is defined by an angle, typically measured in degrees, which determines how far the figure is turned.

Practical Tip

• Visualize the rotation by using a protractor to measure angles accurately.

Step 2: Determining the New Coordinates After Rotation

To find the new coordinates of a point after rotation around the origin, use the following formulas based on the angle of rotation (θ):

• For a 90-degree rotation counterclockwise:

  • New coordinates: (x', y') = (-y, x)

• For a 180-degree rotation:

  • New coordinates: (x', y') = (-x, -y)

• For a 270-degree rotation counterclockwise (or 90 degrees clockwise):

  • New coordinates: (x', y') = (y, -x)

Example

• If you have a point A at (3, 4) and you want to rotate it 90 degrees counterclockwise:
  • New coordinates would be (-4, 3).

Step 3: Applying Rotation to a Shape

1. Identify the vertices of the shape you want to rotate.
2. Choose the angle of rotation, either 90, 180, or 270 degrees.
3. Apply the rotation formulas to each vertex to find the new coordinates.
4. Plot the new vertices on a graph to visualize the rotated shape.

Common Pitfalls

• Ensure the rotation direction is correct (counterclockwise is standard).
• Double-check calculations for each vertex to avoid errors.

Step 4: Practice with Examples

• Try rotating different shapes (like triangles or squares) using various angles.
• Verify your results by comparing with expected outcomes or using graphing tools.

Conclusion

In this tutorial, we covered the fundamental aspects of rotation in geometry, focusing on how to determine new coordinates for points after rotation around the origin. Practice is key to mastering this concept, so continue to experiment with different shapes and angles. For further learning, you can explore related topics such as translation and reflection in geometry.