What is a Translation in Geometry?
A translation is a process of moving an object in a given direction. It may be a positive or negative movement. The direction of translation is usually a function of the original shape.
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There are many methods of translating shapes. One way to do this is by using a reflection. This involves flipping a figure over a line that has a symmetry to the original. Another method is a passive transformation, which does not alter the figure but merely moves its coordinate system. When done correctly, the result is a semblance of a new shape.
The most important element of a good translation is its resemblance to the original. This can be accomplished by applying rules to the points of the original. Using the right notation and math, you can get the same results. For example, if the x-coordinate of a triangle is XYZ, and the y-coordinate is Y’, you can calculate the new Y’ by adding C to the old Y. If you want to do it the other way around, you can plot the new x and y coordinates as per the curve shape.
In the geometry world, a translation is often considered to be a subset of the more formal and esoteric motion of translation. However, when it comes to the ol’ school of thought, the translation is a purely functional, albeit active, process.
It is also a measure of the relative magnitude of a change in position of an object. For instance, a triangle that has been translated left by k units is a triangle whose vertices have been changed by k. Translation can also occur horizontally, vertically and even in both directions at the same time.
Depending on the nature of the translation, the corresponding measure of success could be an array of a varying degree. Hence, it is not surprising that the name is a shortened form of the Latin word for carry across. Often, a translation can be defined as the addition of a constant vector to each point of the original object.
Other types of translation include parallel and circular. Parallel translation involves the use of a parallel reflecting line. These are perpendicular to the translation line and have a minimum distance of about half the translation distance. Similarly, circular translation is the result of a circle being flipped about an imaginary axis. Using parallel lines is a good idea if you plan to perform a number of translations in a short space of time.
An image is a figure that is similar to the original. Likewise, a pre-image is a shape that was present before a figure is transformed. Usually, a hand is pictured on a flat surface to illustrate this. Typically, the pre-image is labeled with uppercase letters while the corresponding image is the nth letter. Occasionally, the nth letter is rearranged to display the image.
Whether you are a budding amateur or a professional working in the field of mathematics, you will have to do a little experimenting to learn how to do a proper translation.