TRANSFORMASI (PART 3) : DILATASI : MATEMATIKA KELAS 9 SMP

Introduction

This tutorial aims to provide a clear understanding of dilatation, a key concept in transformations studied in mathematics, particularly for 9th-grade students. Dilatation refers to the resizing of shapes while maintaining their proportions. This guide will break down the steps involved in performing dilatation, making it easier for students to grasp the process and apply it in their studies.

Step 1: Understanding Dilatation

• Definition: Dilatation is a transformation that alters the size of a figure while keeping its shape and proportions intact.
• Scale Factor: The amount by which a figure is enlarged or reduced is called the scale factor.
  • A scale factor greater than 1 enlarges the figure.
  • A scale factor between 0 and 1 reduces the figure.

Step 2: Identifying the Center of Dilatation

• Choose the Center: Decide on a point in the plane, referred to as the center of dilatation. This point serves as a reference for resizing the figure.
• Graphing: On a coordinate plane, plot the center of dilatation clearly so that you can visualize the transformation.

Step 3: Applying the Scale Factor

• Identify Original Coordinates: Take the coordinates of the vertices of the original shape. For example, if your shape is a triangle with vertices A(2, 3), B(4, 5), and C(6, 7), note these down.
• Calculate New Coordinates: Use the formula to find the new coordinates based on the scale factor (k):
  • New coordinate = Center + k × (Original coordinate - Center)
• Example:
  • If the center of dilatation is O(1, 1) and k = 2:
    • New A = (1 + 2 × (2 - 1), 1 + 2 × (3 - 1)) = (3, 5)
    • New B = (1 + 2 × (4 - 1), 1 + 2 × (5 - 1)) = (7, 9)
    • New C = (1 + 2 × (6 - 1), 1 + 2 × (7 - 1)) = (11, 13)

Step 4: Drawing the New Figure

• Plot New Points: On the same coordinate plane, plot the new coordinates calculated in the previous step.
• Connect Points: Draw the new figure by connecting the new points. This visual representation helps in understanding the transformation.

Step 5: Analyzing the Transformation

• Compare Sizes: Observe how the new figure relates to the original figure. Check for proportionality in lengths and angles.
• Verify: Ensure that the figures are similar, maintaining their shapes and angles, but differing in size.

Conclusion

Dilatation is a fundamental concept in geometry that allows for the resizing of shapes while preserving their properties. By understanding the steps to apply dilatation, students can effectively tackle related problems in their mathematics coursework. Practice with different shapes and scale factors to become more confident in using this transformation. As a next step, try applying dilatation to various geometric figures and explore different centers of dilatation for a comprehensive understanding.