(LENGKAP) TRANSFORMASI GEOMETRI - Translasi, Refleksi, Rotasi dan Dilatasi

Introduction

This tutorial covers the fundamental concepts of geometric transformations, including translation, reflection, rotation, and dilation. Understanding these transformations is essential for studying geometry, as they are widely used in various fields, including art, engineering, and computer graphics.

Step 1: Understand Translation

Translation involves moving a shape from one location to another without changing its size, shape, or orientation.

• Identify the shape you want to translate.
• Determine the direction and distance of the translation.
• Move each point of the shape the same distance in the specified direction.

Practical Tip: Use a coordinate system to visualize the translation; for example, moving a point (x, y) to (x + a, y + b), where a and b are the distances moved along the x and y axes, respectively.

Step 2: Learn Reflection

Reflection creates a mirror image of a shape across a specific line, known as the line of reflection.

• Choose the line of reflection (e.g., the x-axis, y-axis, or any other line).
• For each point on the shape, measure the distance to the line of reflection.
• Place the reflected point the same distance on the opposite side of the line.

Common Pitfall: Ensure that you maintain the same distance from the line of reflection for each point to achieve an accurate reflection.

Step 3: Explore Rotation

Rotation involves turning a shape around a fixed point, known as the center of rotation.

• Identify the center of rotation and the angle of rotation (e.g., 90°, 180°, or 270°).
• For each point on the shape, determine its new position after the rotation.
  • Use the rotation formulas if rotating around the origin:
    • For a point (x, y) rotated by θ degrees:
      • x' = x * cos(θ) - y * sin(θ)
      • y' = x * sin(θ) + y * cos(θ)

Practical Tip: Visualize the rotation using a protractor to ensure accuracy.

Step 4: Understand Dilation

Dilation alters the size of a shape while preserving its proportions and angles. It involves stretching or shrinking the shape from a center point.

• Identify the center of dilation.
• Determine the scale factor (greater than 1 for enlargement, between 0 and 1 for reduction).
• For each point (x, y) of the shape, calculate the new coordinates as follows:
  • x' = center_x + scale_factor * (x - center_x)
  • y' = center_y + scale_factor * (y - center_y)

Real-World Application: Dilation is commonly used in design and architecture to create scaled models.

Conclusion

In this tutorial, we explored four key geometric transformations: translation, reflection, rotation, and dilation. Each transformation has its unique properties and applications. To practice, try applying these concepts to different shapes and scenarios, enhancing your understanding of geometry in real-world contexts. For further learning, consider exploring more complex transformations or integrating these concepts into artistic projects.