rotasi matematika kelas 9 (mudah); [materi ke-3] bab transformasi

Introduction

This tutorial covers the concept of rotation in mathematics, specifically designed for 9th-grade students. It provides clear steps and examples to help you understand how to perform rotations in a coordinate plane. By the end of this guide, you will have a solid grasp of the principles of rotation and be able to apply them in various mathematical problems.

Step 1: Understanding Rotation

• Definition: Rotation refers to turning a shape around a fixed point, known as the center of rotation.
• Degrees of Rotation: The rotation can be measured in degrees (90°, 180°, 270°, 360°, etc.).
• Direction: Rotations can be clockwise or counterclockwise.

Practical Tip

Always identify the center of rotation before performing any calculations.

Step 2: Identifying the Center of Rotation

• Choose a point in the coordinate plane around which you will rotate the shape. Common centers include:
  • The origin (0,0)
  • A vertex of the shape
  • Any other specific point

Example

For example, if you are rotating triangle ABC around point A, point A will remain fixed while points B and C will move.

Step 3: Rotating Points

To rotate a point (x, y) around the origin (0, 0), use the following formulas based on the angle of rotation:

• 90 degrees counterclockwise: (x, y) → (-y, x)
• 180 degrees: (x, y) → (-x, -y)
• 270 degrees counterclockwise (or 90 degrees clockwise): (x, y) → (y, -x)

Example Calculations

1. Rotate point (2, 3) by 90 degrees counterclockwise:
   • New coordinates: (-3, 2)
2. Rotate point (4, -1) by 180 degrees:
   • New coordinates: (-4, 1)

Step 4: Rotating Shapes

• To rotate a shape, rotate each of its vertices using the formulas discussed.
• Once all points are rotated, connect them in the same order to form the new shape.

Practical Advice

• Sketch the original and rotated shapes to visualize the transformation.

Step 5: Practice Problems

Try rotating the following points and shapes:

1. Rotate the point (1, 2) by 90 degrees counterclockwise.
2. Rotate the triangle with vertices at (1, 1), (2, 1), and (1, 2) by 180 degrees around the origin.

Common Pitfall

Always double-check your calculations, especially the signs of the coordinates after rotation.

Conclusion

Understanding rotation is crucial for mastering geometric transformations. Practice rotating points and shapes to reinforce your learning. Consider exploring additional resources or practice problems to further enhance your skills. Remember, the more you practice, the more comfortable you will become with these concepts. Happy studying!