TRANSLASI (PERGESERAN) || TRANSFORMASI GEOMETRI

Introduction

In this tutorial, we will explore the concept of geometric transformations, focusing specifically on translation. Understanding translation is essential as it lays the groundwork for more complex transformations such as reflection, rotation, and dilation. This guide will help you grasp the key principles of translation and how to apply them effectively.

Step 1: Understanding Translation

Translation refers to moving every point of a shape or object a certain distance in a specified direction. This transformation preserves the shape and size of the object but changes its position.

Key Concepts

• Vector: A translation can be described using a vector, which has both direction and magnitude. For instance, moving a shape 3 units right and 2 units up can be expressed as the vector (3, 2).
• Coordinates: The original coordinates of the shape will change based on the translation vector.

Step 2: Applying Translation to Points

To translate a point in a coordinate system, follow these steps:

1. Identify the Original Coordinates:

   • Let's say we have a point A at coordinates (x, y).

2. Determine the Translation Vector:

   • For example, if the translation vector is (3, 2), this means you will move the point 3 units to the right and 2 units up.

3. Calculate the New Coordinates:

   • Apply the translation by adding the vector to the original coordinates:
     • New x-coordinate = x + 3
     • New y-coordinate = y + 2
   • For point A (2, 3), the new coordinates will be:
     • New A = (2 + 3, 3 + 2) = (5, 5)

Step 3: Translating Shapes

To translate an entire shape, apply the same translation vector to each vertex of the shape.

Example:

• Consider a triangle with vertices A(1, 1), B(2, 3), and C(3, 1).
• If we translate this triangle using the vector (2, 1):

1. Calculate new coordinates for each vertex:

   • A' = (1 + 2, 1 + 1) = (3, 2)
   • B' = (2 + 2, 3 + 1) = (4, 4)
   • C' = (3 + 2, 1 + 1) = (5, 2)

2. The new triangle will have vertices A'(3, 2), B'(4, 4), and C'(5, 2).

Step 4: Visualizing Translation

To better understand translation, it can be helpful to visualize the process:

• Use graph paper or a digital graphing tool.
• Plot the original points or shapes.
• Use a ruler to apply the translation vector and plot the new points.

Conclusion

Translation is a fundamental concept in geometry that involves moving points and shapes in a coordinate system. By understanding and applying translation, you will be better equipped to tackle other transformations like reflection, rotation, and dilation.

Next Steps

• Practice translating different shapes and points using various vectors.
• Explore the other types of transformations mentioned, such as reflection and rotation, to expand your understanding of geometric transformations.