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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.
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Translation is a transformation that shifts a figure on a plane without changing its size, shape, or orientation
The pre-image is the original figure before translation, and the image is the figure after translation
Translation involves moving every point of a figure consistently to maintain its intrinsic properties
Translations are executed by altering the coordinates of a figure's points in a coordinate system
Specific mathematical rules govern the process of translation to ensure uniformity across the entire figure
The general formula for translation is g(x, y) = (x + h, y + k), where h and k represent the horizontal and vertical shifts, respectively
Horizontal translation involves adding or subtracting a fixed value to the x-coordinates of a figure's points
Vertical translation involves adding or subtracting a fixed value to the y-coordinates of a figure's points
When a figure undergoes both horizontal and vertical translations, the combined effect is represented by the function g(x, y) = (x + h, y + k)
To apply translation to a geometric shape, one must systematically adjust the coordinates of each vertex according to the translation vector's components
The translation of individual points follows the same principles as those for entire shapes
Real-world examples, such as translating a rectangle or triangle, effectively demonstrate the concept of translation
To determine the translation between a pre-image and its image, one must compare the coordinates of corresponding points
The difference in the x-coordinates gives the horizontal component of the translation, while the difference in the y-coordinates provides the vertical component
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.
