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Translation math

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In general language translation means to translate the code or language in other language for better communication. Translation is mainly used to convert an object from a form to another form. We can see this term Translation in various fields as in physics, chemistry and in maths.
When it is about the translation Math, then it means to slide, to move, displacement etc. In translations math when an object slides from its original location to the destination location then it is called as translation in math. The object we are moving must have some shape or some structure in the space. These objects definitely occupy some area or space in original space. When we drag an object, from its original Position to the desired destination position then we find the difference in its coordinates only. There is no change in its shape.
It is very important to remember that one can only drag or slide the object, we cannot rotate it, we cannot resize it we cannot flip it anyways. Then it will not be counted in translation. If there are some coordinate, in which the object is placed say a, b and c when we move the object from its origin to destination coordinates then there will be a change in coordinates. The new coordinates we get will be a', b' and c' . The sign (') is called prime sign. So variables are called as a prime, b prime and c prime.

Translated object have some properties:
Property 1: If an object is translated then it will be congruent to that object, means it will have the same shape as the image object.
Property 2: If an object is translated then it will be having the same vertex as its original vertex, but with the slide movement. These objects will be parallel in space.
Translation in math always represents the sliding or displacement of an object.

Translation Matrix

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In general way, a matrix can be defined as a Set of similar type of Numbers, symbols, integers, etc. When set of these elements are arranged in the form of rows and columns, then this arrangement is called as matrices. We can perform many operations on matrices like we can add elements of two or more matrices; we can subtract one matrix elements from other but the matrix should be of same type.
In order to multiply the matrices the column number of first matrix should be equal to the number of rows of another matrix then only we can multiply two matrixes and get another matrix as a result.
A matrix can either be rotated or translated. Other name of Rotated matrix is Rotation Matrix and translated matrix is also called as translation matrix. The combine form of these two matrixes is called transform matrix.
Here we will discuss the translation matrix. When we get the matrix from transform matrix by doing the space transformation, that matrix is called translation matrix. This translation matrix is denoted by (T). The relation between rotation matrix translation matrix and transform matrix is given as:
R-T = Tr,
Here R is rotation matrix and Tr is transform matrix. In matrix translation, there is a shifting of coordinates only in 2D, this shifting is performed from initial space to the destination space.
Do you know how to find translation matrix? The steps mention below are used for the same:
Step 1: Identify two matrix and their variables.
Step 2: Identify the coordinates of variables.
Step 3: Form the matrix.
Step 4: Do the above three steps for image matrix as well.
Step 5: Coordinates of first matrix + coordinates of image matrix = coordinates of translation matrix.
Step 6: Coordinates of image = coordinates of translation matrix + coordinates of pre image.
Step 7: We get the same matrix we had before by applying these steps.