Matematika Kelas 9 : Transformasi Geometri (part 1 : Translasi)

Introduction

This tutorial covers the concept of geometrical transformations, specifically focusing on translation as discussed in the video "Matematika Kelas 9: Transformasi Geometri (part 1: Translasi)". Understanding translation is essential for students in grade 9 as it lays the groundwork for more complex transformations like reflection and rotation, which will be explored in subsequent videos.

Step 1: Understanding Translation

Translation refers to moving a shape from one position to another without changing its size, shape, or orientation. Here’s how to visualize and understand translation:

• Definition: A translation moves each point of a shape the same distance in the same direction.
• Vector Representation: The movement can be represented by a vector, which has both direction and magnitude.
  • Example: A translation vector can be expressed as (x, y), indicating how much to move in the x-direction and y-direction.

Practical Tip

To visualize translations, draw a grid and plot a shape, such as a triangle. Then apply a translation vector to see where the shape moves.

Step 2: Applying Translation

To apply translation to a shape, follow these steps:

1. Identify the Original Coordinates: Note the coordinates of each vertex of the shape.

   • Example: For a triangle with vertices A(1, 2), B(3, 4), and C(5, 1).

2. Choose a Translation Vector: Decide on the vector you will use for the translation.

   • Example: Use the vector (2, 3).

3. Calculate New Coordinates: Add the translation vector to each vertex's coordinates.

   • For vertex A:
     • New A = (1 + 2, 2 + 3) = (3, 5)
   • For vertex B:
     • New B = (3 + 2, 4 + 3) = (5, 7)
   • For vertex C:
     • New C = (5 + 2, 1 + 3) = (7, 4)

4. Plot the New Shape: Draw the new shape using the new coordinates.

Common Pitfalls

• Ensure you add the vector correctly to each coordinate.
• Double-check the direction of the vector to avoid incorrect placements.

Step 3: Visualizing Translation

Visualization helps in understanding how shapes move. Here’s how to practice:

• Graphing: Draw the original shape and the translated shape on a coordinate grid.
• Using Software Tools: Utilize graphing tools or apps to visualize the translation dynamically.

Conclusion

In this tutorial, we covered the basics of translation in geometry by defining the concept, applying a translation vector to a shape, and visualizing the results. To further your understanding, practice with different shapes and translation vectors. Next, explore reflection and rotation transformations to expand your geometrical transformation skills.