Summary  
This chapter describes implementing geometric translation by adding a fixed (dx, dy) vector to each point in a polygon to shift its position.

General domain of usage  
Computer graphics

**Video Description:** This video demonstrates how translating a polygon shifts its position on the plane. You will see a shape plotted using `matplotlib`, then watch as it moves smoothly to a new location after applying a translation vector.

Translation is a **fundamental geometric transformation** that shifts every point of a shape by the same distance in a specified direction. Mathematically, translating a shape means **adding a fixed vector to each of its points**. 

- If a point has coordinates ` (x, y) ` and you want to move it by a vector ` (dx, dy) `, the new coordinates become ` (x + dx, y + dy) `. This operation preserves the **size**, **shape**, and **orientation** of the figure—it simply moves the entire shape to a new location.

Suppose you have a triangle with vertices at ` (1, 2) `, ` (3, 5) `, and ` (5, 4) `. If you translate this triangle by the vector ` (2, -1) `, the new vertices will be ` (3, 1) `, ` (5, 4) `, and ` (7, 3) `. Each vertex is shifted to the right by 2 units and down by 1 unit. This simple addition works for any shape represented as a collection of points.

def translate_polygon(polygon, dx, dy):
    """
    Translates a polygon by a vector (dx, dy).

    Args:
        polygon: List of (x, y) tuples representing the polygon's vertices.
        dx: Translation in the x-direction.
        dy: Translation in the y-direction.

    Returns:
        List of (x, y) tuples representing the translated polygon.
    """
    return [(x + dx, y + dy) for (x, y) in polygon]

# Example usage:
triangle = [(1, 2), (3, 5), (5, 4)]
translated_triangle = translate_polygon(triangle, 2, -1)
print("Translated triangle:", translated_triangle)


**Which of the following statements about translation is correct?**

Learn the fundamentals of geometric modelling using Python. Explore how to represent, manipulate, and approximate geometric figures programmatically. This course covers basic shapes, transformations, and practical approximation techniques, making geometric concepts accessible and interactive.

Get started with the core concepts of geometric modelling and how Python can be used to represent and manipulate basic shapes.

Delve into geometric transformations such as translation, rotation, and scaling, and see how they affect shapes in Python.

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Translation of Shapes