DILATASI (PERKALIAN) || TRANSFORMASI GEOMETRI

Introduction

This tutorial covers the concept of dilation in geometry, a key transformation that enlarges or shrinks shapes. Understanding dilation is essential for students, particularly those in grade 9, as it builds upon previous topics like translation, reflection, and rotation. Let's dive into how dilation works and how you can apply it to geometric figures.

Step 1: Understanding Dilation

Dilation is a transformation that alters the size of a shape while maintaining its proportions. Here are the key components:

• Center of Dilation: This is the fixed point in the plane about which all points of the shape are expanded or contracted.
• Scale Factor: A number that determines how much the shape will grow or shrink.
  • If the scale factor is greater than 1, the shape enlarges.
  • If the scale factor is between 0 and 1, the shape reduces in size.

Practical Tip

When visualizing dilation, consider a simple example. If you have a triangle and you dilate it with a scale factor of 2 from the origin, each vertex of the triangle will move away from the origin, doubling its distance.

Step 2: Performing Dilation on a Shape

To perform dilation on a geometric shape, follow these steps:

1. Identify the Center of Dilation: Choose a point that will remain fixed during the transformation. This could be the origin (0,0) or any other point on the coordinate plane.

2. Determine the Scale Factor: Decide how much you want to enlarge or reduce the shape. For instance, if you choose a scale factor of 3, the new shape will be three times larger than the original.

3. Calculate the New Coordinates:

   • For each vertex (x, y) of the shape, apply the formula:
     • New x = Center x + Scale Factor × (x - Center x)
     • New y = Center y + Scale Factor × (y - Center y)

Example

If you have a triangle with vertices A(1, 2), B(3, 4), and C(5, 6), and you are dilating it from the origin (0,0) with a scale factor of 2:

• For point A:
  • New A = (0 + 2 * (1 - 0), 0 + 2 * (2 - 0)) = (2, 4)
• Repeat for points B and C to find their new positions.

Step 3: Visualizing the Dilation

Drawing the original and the dilated shape can help you understand the transformation better:

• Sketch the original shape and its vertices.
• Use the new coordinates calculated from the previous step to plot the dilated shape.
• Connect the new vertices to form the dilated shape.

Common Pitfalls to Avoid

• Forgetting to maintain the same proportions when calculating new coordinates.
• Choosing an inappropriate center of dilation that distorts the shape excessively.
• Miscalculating the scale factor leading to incorrect size changes.

Conclusion

Dilation is a fundamental concept in geometry that allows for the resizing of shapes while preserving their proportions. By understanding the center of dilation and the scale factor, you can effectively apply this transformation. Practice by dilating various shapes and exploring different scale factors. This foundational skill will enhance your understanding of geometric transformations as you progress in your studies. Happy learning!