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Translation in Geometry

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Geometric translation is a transformation that shifts a figure on a plane without altering its size, shape, or orientation. This text delves into the execution of translations using coordinate systems, formulating mathematical rules for precise movements, and implementing these on various shapes. It also provides real-world examples to illustrate the concept, highlighting the importance of maintaining the integrity of a figure's geometry during translation.

Exploring Translation in Geometric Terms

Translation in geometry is defined as a type of transformation that shifts a figure by a certain distance in a specified direction on a plane. This operation does not change the figure's size, shape, or orientation. The term 'pre-image' refers to the original figure before the translation, and the 'image' denotes the figure after the translation has been applied. It is essential to understand that translation involves moving every point of the figure consistently, ensuring that the figure's intrinsic properties remain unchanged.
Red triangles, blue squares, and green circles in horizontal rows with uniform spacing on a white background, showcasing pattern repetition.

Executing Translations Using Coordinate Systems

In a coordinate system, translations are executed by altering the coordinates of the figure's points. This system provides a structured way to describe the positions of points and to apply transformations. For a translation, the coordinates of each point in the pre-image are adjusted by adding or subtracting a fixed value, resulting in the coordinates of the translated image. This process is governed by specific mathematical rules that ensure the translation is performed uniformly across the entire figure.

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00

The original shape before undergoing a translation is called the ______, while the shape after the translation is known as the ______.

pre-image

image

01

Translation effect on figure's points

Each point's coordinates adjusted by adding/subtracting fixed value.

02

Translation uniformity requirement

Mathematical rules ensure consistent translation across entire figure.

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